Teenagers Andy Robertson, John Souttar and Ryan Gauld are at the heart of the United side along with Scotland Under-21 captain Stuart Armstrong.
Facing Rangers at Ibrox might be daunting for some young players but Dailly feels manager Jackie McNamara has created the ideal platform for them.
Dailly, who made his first-team debut for United at the age of 16, said: "The way I see them and the way Jackie McNamara seems to have looked after them, these big stages almost tend to be fun for them. They are allowed to go and express themselves and it looks like it's a bit of fun for them.
"Sometimes the game can be so big that nerves go out the window. Sometimes league matches can be more nerve-racking and it feels a bit more tense, and you need a result and feel a bit tired.
"These boys will be fully rested and fully ready. If any young lads don't play well this weekend, it's probably because Rangers have done their homework and manage to stop them."
Dailly was only 20 when he helped United to their greatest win over Rangers, when Ivan Golac's unorthodox preparations helped them to a Scottish Cup final win in 1994.
"It was all the stuff at the time about smelling the flowers and going for walks," the former Scotland player said.
"We were just resting up and he told us to go and express ourselves. To do that, you have got to be relaxed and confident that your manager is allowing that, to go out and have nothing to lose. It definitely had a big effect on us.
"They have got more structure under Jackie in the positions they play and the way they are coached at the club in general, the whole thing seems set up to allow them to do go out and use their ability."
Dailly was speaking on behalf of TSB, sponsor of the Scotland Under-18 Schoolboys team, who face England in the Centenary Shield at Ewood Park on Friday.
Speaking of his own experience with Scotland Schoolboys, he said: "It was fundamental. I probably represented Scotland at all levels more than 150 times and for me it was the ultimate.
"We won the Victory Shield and beat England in our last game at Old Trafford. I've got such vivid memories of that game - Nicky Barmby and Ryan Giggs played for them.
"If they get a result there or shine, they will just never forget that."