If you did decide to do barrels (I'm not for it, but it is your horse) I'd recommend a vet check first. Point out her back, have them do a thorough exam. If they give you the go ahead, then you'd need to start with LOTS and LOTS of walking and trotting. How often do you trail ride? To be fit for barrels, she'd need to build up to 30+ minutes of straight trotting.
Can she do a flying lead change? If not, you'll need to teach her to change leads quickly and accurately. Start doing serpentines and circles, gradually making them tighter and tighter. Do some canter work and build her up to 5-10 minutes of cantering. Teach her to yeild her hindquarters, bend into her circles, and teach her to stay in frame. That's the only way you're going to improve her topline.
The biggest fault I see in barrel horses is that they're underdeveloped and hold their heads high when they're running. You'll want hers down and her body rounded, to counteract her back. Once she can do all of that and can canter for a while without being too winded, then I'd get another vet check, and begin her barrel training.