The gates of George Square Gardens in Edinburgh open at 10am sharp, although most Fringe comedians and performers will never have been there at that – to them – unearthly hour.

Remarkably enough there is such a thing as a morning Fringe, though. It's a world of coffee-cups, pastries and babycinos, frequented by the parents of young children – those, for instance, in the snaking buggy queue outside Monski Mouse's Monster Baby Disco Dance Hall, or the small gathering nearby of three stage veterans, Nina Conti, Ali McGregor and Lucy Porter. These three sip coffee and exchange anecdotes about baby-led weaning, vegetables, playparks and breast-feeding around shows. Every now and again they glance at their children, one-year-old Drummond, two-year-old Beatrice and eight-month-old John respectively. Ali McGregor tells her daughter Beatrice, who clutches an inflatable Minnie Mouse, that mummy will come and join the disco shortly. And what comes out of wide-ranging babytalk, is that being a stand-up or Fringe performer, is a perfect career for a mother.

Often, it seems as if stand-up is the domain of the young, of the perpetual student, the Peter Pan happy to spend August on a bender. No space, one might think, for baby in tow. Stand-up Lucy Porter notes that before this Festival – her first with the two children she squeezed out in such quick succession she once said she had been "on maternity leave for 18 of the last 24 months" – she had never been up before 11am in Edinburgh. She had never seen a show before 2pm. "I didn't know daylight existed. Now I'm up at 4am with my youngest- Hopefully it's just a phase."

Get together any group of mothers and you'll find their parenting approaches will be wildly different, but what's remarkable about these three is how much they share. There is, for instance, no one following Gina Ford's contented baby programme here, with its strict routines. Porter and burlesque singer Ali McGregor may get locked into discussing The Baby Whisperer book and daily rhythms that sound vaguely like routines – bed-time for baby, then out to a gig – but Porter points out: "There's no way you can be a performer and do Gina Ford." This is not to say that their children spend August on a merry-go-round of parties, shows and late-night bars. Though ventriloquist Nina Conti confesses going to the odd party with her first child – "I think that was because I was a moron" – mostly what they appreciate is the calmer flow of the Fringe, "not over-doing it".

Meanwhile, all share white knuckle tales of trying to breastfeed before and after shows, anecdotes like McGregor's description of an Assembly Rooms launch when her daughter was three months old. Confronted with a communal backstage dressing room, but needing to feed Beatrice, she found a smaller room and started "breastfeeding and curling my hair at the same time". Someone came in and declared, "This is my dressing room." McGregor says: "I had a real meltdown. I was just a monster. After that I remember carrying the pram up all the stairs in Assembly Hall, with her in it and no one helped me. I was so losing the plot. And then I had to get out there and sing happy songs."

There are stories, too, of long-haul plane journeys, of the strain of being away for a gig, or, as Conti recalls, finding you have missed a flight home. "I wept in the airport," she says, "I was so upset because I had thought I would get back to my son in the night and get in to bed with him and that would be nicer than arriving in the morning." Often, she says, she found it tough to leave her older son Arthur even for just an evening gig. "I used to make quite a big deal of leaving him. I don't think I said goodbye very well, I couldn't say it casually, I'd over-do it. And it so makes the difference the way you deal with it – it's a complete reflection of that."

But what is remarkable, also, is that coming back after such a life-changing event as having a child, these performers are at the top of their game. Many believe Porter's show, People Person, is the best she has done. Our own critic, Barry Didcock described it as a "winning return", "a perfectly circular comedy routine that goes out with a killer punchline". McGregor got a Fringe First award for her post-baby return show. Conti, who has been a parent for eight years, won the Barry Award at the Melbourne International Comedy Festival in 2008. They are racking up five-star reviews, while also being there when their little ones wake up, take their first steps, graduate from nappy to potty, have a mid-morning meltdown. Conti, says she's never had a nanny or childminder. "I didn't want anyone else looking after him. I thought, 'This the most important thing in my life. I'm going to give everything to him.' I was really full on. I have quite an intense kid as a result." She adds, however: "But I've only managed it because I have an incredibly supportive mother and husband." Indeed, it seems to help that they are all married to performers, McGregor to comedian Adam Hills, Porter to writer and actor Justin Edwards and Conti to stand-up Stan Stanley.

There's a way in which their working lives seem to feed into their time with children. McGregor talks of singing to her daughter, and has toyed with the idea of doing a show based around distorted nursery rhymes. Porter runs a "mother and baby" comedy club, where mums can bring along kids under one year old, perform and have a laugh. Conti, meanwhile, sees Monkey, the famously dirty-mouthed character she has described as "a stinky little puppet", as part of the family. Often she gets him out to play with her younger son. "Drummond loves Monkey, don't you?" she says. She adds that he's a "very different Monkey from the one on stage", a kind of calmer, gentler alter ego. "There's something about the way I can talk to Drummond with Monkey which is really educational. I can say, 'What's that?' And monkey will say, 'I don't know.' Then Drummond will say, "a frog".

This is not to say the parental juggling-act has been easy. Conti recalls doing a show when Drummond was six weeks old. She says: "I don't remember it. I was still in a hormonal fug, on autopilot. I got away with it but I don't really remember that time."

Given the pressure on female performers to look good, to return with extra pounds of babyweight or a southwards shift of a few curves, can be angst-inducing. McGregor describes a performance when her daughter was three months old and a woman came up to her and said, "I'm sorry, but I think you need a more supportive bra." "It was," she says, "about the worst thing I could have heard because I was really self-conscious, I was wearing this voluminous dress and a fascinator in my hair hoping that it would draw attention away. I was literally breast feeding before I went on stage and breast feeding afterwards." Around the same time, attending a television awards ceremony with her husband, Adam Hills, she recalls standing behind Dannii Minogue just after the singer and TV presenter had given birth. "I wanted to stab her in the back. Why are you making me feel like I'm a failure?"

But all three feel that motherhood has freed them from that pressure to look a particular way. Conti says: "I remember when I started working I thought it was all about being a young girly girl with a monkey and the juxtaposition of those two things. I thought when I lose my looks I'm going to lose my career but that sort of thing is so misconceived and bad for your comedy." As Porter puts it, "It's liberating to go I just couldn't give a s*** because I've really got more going on now."

Indeed, this is one of the themes running through their thoughts. Since motherhood blasted into their lives, there has been less time for angst. Pre-baby, says McGregor, a typical festival would involve little during the day, other than looking at reviews and analysing your show, often "while you're the worse for wear". Now there isn't even "space", as Porter puts it, in their heads for that. Conti, who did her first Fringe show as a mum when Arthur was three, says: "Your career becomes important not through any sense of ego but you have to provide for your children. You're quite pragmatic about it."

Because of this, the Fringe is actually more enjoyable. With children along, they are having a ball. Only McGregor has ever left her daughter behind and regretted it. She recalls coming to Edinburgh for a week, while her daughter stayed with Hills: "I actually had the worst Edinburgh I've ever had last year. I just didn't enjoy myself. I missed her."

Nina Conti is at the Pleasance Dome till August 27, Ali McGregor is appearing at Assembly George Street Gardens till August 27 and Lucy Porter is at The Stand One till August 26