My mate competes reguarly on her 14.3hh QH mare, bred as a cutter and has short fat front legs, big round body etc. (barrell on legs ;)
This mare works really REALLY nicely, she's started walk pirouettes and usually works lovely and through. She does struggle a little in canter though to sit ove rher hind end, but thats about her only downfall. Movement isn't that great but at least my mate can learn all the basics on her in a correct manner.
She doesn't do brilliantly at comps, but it's not because the horse isn't correct, it's because she's up against very well bred and flashy warmbloods that of course will look better to the judge, her horse just doesn't have the movement to be up there with the best. However, in pony/riding club comps, she wins just about everything on her, because she's so lovely and soft.
There's absolutely no reason why you can't do some dressage work with your QH, even if you don't go out and place in everything, you can still get a QH working correctly, even if they are built like little tanks!!