My gelding is pretty fit, but he had troubles cantering decent on the lunge line (and in the saddle) for more than a few strides. I would say work on trotting and cantering on the lunge line, build up to where she can canter in smaller circles and hold it for a few laps. I started out slow with my gelding. If he would give me three good strides of canter, he got praised and rubbed and he was happy to know he did it right. From there he caught on, and not only was mentally willing, but after a while he was more physically capable of supporting himself.
Once you know she is physically capable of doing it, it is time for you to come into play. I'm working on sitting the canter now, too, and these are some helpful tips I've gotten in the past years. If you can, ride with one hand, and put the other on the saddle horn. Don't clench onto it and hold yourself forward, sit back and push back on the horn - push yourself into the saddle. Put your reins in one hand, and push on the saddle horn at the trot, get a feel for it, then ask for the canter. Give her enough of her face where she can use her body. Getting used to holding her tight isn't going to help you out in the long run, nor teach her to use herself properly and trust you. Make sure to move your hips with her, and it will come with more and more practice.
Just like she had to build the muscle memory to canter, you do as well. When I worked on this at a clinic in a huge out door arena, their were plenty of times that I had to stop and keep myself from tipping too far to one side. It would only take one bouncy stride to get a little out of place. Get someone who is knowledgeable that you can trust to help you and give you pointers. Practice with other, trained horses who don't have perfect canters, but you know they won't kill you if you're flopping around. Good luck. :)