A thing you should take into consideration - drafts and draft crosses grow and mature very slowly. At 3, she is still just a baby and might find it hard to balance and move freely with a rider, thus the lack of the "oomph". I wouldn't start cantering her under saddle yet, and spend more time on groundwork (responsiveness in particular, also ground driving can do wonders for riding later in life), relaxation, stretching, walking and trotting up hills in hand and under saddle to build up muscles, straightness. My horse, a light draft, was backed at 4 and had his first canter under saddle as a late 4yo, and he was still pretty compromised by his large, growing body. Now, only at the age of late 6, he has reached the maturity of a grown up horse. I like to take it slowly - there is nothing to miss, and we get healthier horses in the long run, if we wait a bit before asking more from them.
I have come a long way, to surrender my shadow to the shadow of my horse.