I guess I'll be the odd man out and say not to worry about it. She can canter when SHE is ready.
My youngest daughter was afraid to canter. We tried her on Cowboy - a little 13 hand mustang whose trot can make a strong man pee blood, but whose canter is smooth enough to roll a cigarette on. She started screaming. We told her to spread her knees and relax. When she did that, Cowboy slowed down.
Next attempt was on Trooper, our Appy. She said she was ready. I believed her. She applied the right cues...and nothing. Trooper normally will canter if you kiss, but he was NOT going to canter that day! My daughter later admitted she wasn't really ready, and Trooper did what she wanted instead of what she asked.
So we gave up.
About a year later, riding Trooper, she kissed, he shifted into a canter, and we haven't been able to stop her since. She'll canter at the drop of a dime, and Trooper will do it for her. I had to stop her once because the cinch came loose and was hanging 8 inches below Trooper's belly...but they were cantering without a care.
Horses need to learn on their own schedule sometimes, and sometimes kids do as well. Let her work her balance at a trot, changing speeds and doing turns, etc. When she is ready, she'll be ready.
If your daughter doesn't like to lean back, she may be a natural for a forward seat approach to riding. I don't like his chapter on the use of spurs, but Chamberlin's stuff on seat and balance is great:
You could also peruse Common Sense Horsemanship online here: The Common Sense Horsemanship
But their ideas on riding will not agree with your instructor's idea...