Each horse is different, and at 3, yours is still growing and maturing. Her proprioception (ability to know where her feet and other body parts are and what they are all doing at any given time) is still developing.
That being said, I agree with the previous posters about taking it easy. Do lots of walk and trot, work on your transitions without drilling your horse and try to build in some hill work at the walk to help strengthen her back end. When your transitions are smooth and she is confidently balancing around circles at the trot without dropping her shoulder or hollowing her back, you can start asking for the canter along a straight line, but only a few strides at a time.
For example, walk ten strides, trot 5 strides, canter 3 strides down the long side and come back to a walk or trot. Remember to support your mare in the transition so she doesn't nosedive into the walk/trot. You can then start to build the number of canter strides slowly over time. Once she is confidently cantering the long side of the arena, you can start to work on helping her learn to balance through the corner.
Again, just take it slow so your mare has a chance to build her confidence, balance, and musculature the RIGHT way, and you should have years of enjoyment out of her at all gaits.
Good luck!!