This is not prodigy in the style of Linsey Macdonald (breaking the UK senior 400m record at 16), or Jamie Henderson (UK senior 100m champion at 17), whose rise was dotted with titles and records. Muir describes herself as "pretty mediocre" on her arrival at the University of Glasgow in the autumn of 2011 to study veterinary medicine. But her transformation was meteoric. A new coach and training regime produced stunning results.
Within a year she had won eight Scottish titles, ranging from 400m, through 800m and 1500m, to cross-country. Compellingly, her best times for 800m and 1500m are faster at 20 than those of Yvonne Murray and Liz McColgan at the same age and, even more arrestingly, faster than those of Paula Radcliffe and even Kelly Holmes, Olympic champion at both distances in 2004.
"You look back at all-time lists, people's profiles, and what times they did at what age," said Muir yesterday. "It's quite amazing to think I am around these times, and even faster. And to think where they went, and where can I go? I don't know whether I will get to their level, but it's nice to know that, at this stage, I am on track.
"Any athlete's aim is to win Olympic gold, so it's exciting to think it might be achievable. But it's a little intimidating, too. It depends how my first year as a senior goes; it's where most people make it or break it. Let's hope I go down the right path. I'm pretty surprised. I have surpassed a lot of people's expectations, including my own."
A year ago, as Edinburgh's Lynsey Sharp became Britain's sole Olympic 800m choice, Muir's best for two laps was 2min 07.3sec. She was ranked 36th in the UK, but as Sharp battles injury, Muir has improved to 2:00.86, so now she joins Marilyn Okoro and Jessica Judd as the GB choice for the Worlds. "I was hoping just to get on the team for the European Under-23 Championships this year, but to win bronze, and then get to the Worlds – I didn't expect that."
This year Muir won the UK Indoor 1500m senior title and reached the final at the European Indoor Championships in Gothenburg, so perhaps she should not have been too surprised by that under-23 bronze. Last year hinted something outrageous was in the offing. Her brother, Rory, is a promising 800m runner. "I was simply known at the club as Rory's big sister; I had only one gold medal from any Scottish championships, from under-13 to under 20, in cross-country, schools, indoors, outdoors. Everything."
That changed when she joined Glasgow University Athletics Club. The coach there, Active Schools Co-ordinator Andy Young, noted her potential immediately. He was World Schools 800m champion when he was at Boclair Academy, and he has transformed Muir, whose previous athletics existence, at Dundee Hawkhill, "was no more than a hobby - I used to do tap dancing, some hockey, and got halfway to a black belt in karate before running took over. I loved outdoor sport: rock climbing and kayaking. I don't have the time now."
On moving to university, Muir helped the GB junior team to European cross-country gold within months. She took the Scottish under-20 cross-country title at Falkirk a year past February, and the following day won the national indoor 800m title, breaking the Scottish under-20 record which had stood to Linsey Macdonald since 1982. Her versatility knew no bounds: the Scottish Universities' indoor 400m and 800m title on the same day, the Scottish under-20 indoor 400m and 1500m titles on the same day, and the Scottish senior 1500m title outdoors last summer. She was also selected for the 3000m at the World Junior Championships. All before her 20th birthday.
Each personal best has a telling impact on Young. "Laura might win $1000 in a race, but her biggest satisfaction is reminding me that I can't go to McDonald's for a week," he laughs. Young used to join her in repetition runs, "but soon I couldn't keep up – she has forced my retirement and my new physique."
Muir admits he has changed her mindset. "I always wanted to compete in the Commonwealth Games, but I wondered how on earth I could do that. Andy set realistic targets, encouraged me to work harder, and has brought down my times."
From Milnathort, near Kinross, she already has the Glasgow 2014 qualifying standard for both 800m and 1500m. "Maybe I could do a Kelly [Holmes] and do both in Glasgow. It will depend on the timetable. I'd want to perform to my best rather than do mediocrely in both. It's hard to say what my best event is – I am improving so much in both."
She is fourth in Britain this year at 1500m, just outside the world qualifying time. "I'd like to see a bigger improvement before deciding which; 1500 is what I am targeting most just now. Scotland's qualifying times are set on the basis of reaching finals, so I should manage that.
"Podium in 2014? Well, I don't like to set my eyes on something that might not be achievable at the moment. But when next year comes round, I'll see where I am, times-wise and in terms of the competition. It would be amazing if I could."
She says as long as she runs "to the best of my ability in Moscow, I won't be disappointed. I just want to race tactically as best I can".
Her other focus is arranging placements for her studies. "I have been working with cows and sheep at the vet college farm, but I'm trying to arrange another at kennels for a couple of weeks. It's awkward, being away for racing, to find a suitable place."
It helps that the vet college staff includes Doctor Hayley Haining, a prodigious teenage talent once touted as successor to McColgan. It was Radcliffe who overtook Haining as Britain's best finisher in the world junior cross-country, back in 1990, before Muir was born. Yet Haining, now 41, has the marathon qualifying standard for Glasgow 2014 and could be a Commonwealth Games team-mate next year. I have been chatting to her quite a bit, and she has been really helpful," says Muir.