As long as you train correctly, and your horse doesn't have any soundness issues that couldn't stand up to the rigors of cross country, I don't see why not! And those are things that would go for any horse-not just a specific breed. I do dressage with my paint mare, and they aren't exactly known for being dressage horses. I also pop over a few jumps with her now and then. QH's are wonderfully versatile-they may not make it to the top levels of eventing as often simply because of their more downhill build/overall conformation versus that of say, a warmblood, but I think your horse sounds very suited to what you want to learn. Good luck!