Definitely get a QH, they are awesome, I just jumped my 3'6". Make sure, you find one with English conformation (shorter back, nice shoulder and pasturn angles, proper knees and hocks) vs a pleasure QH.

I used to jump a 23 year old QH gelding! I love quarters because of how versatile they are, we could do Gymkhana one day then jumping the next, then pleasure/equitation the next! With other people he was jumping 3.5ft+ in his 20s (he didn't do it very often and he wasn't my horse, just the lesson horse I used to ride)