When it comes down to it, your horse is taking you where you want to go, doing the kinds of things you want to do, “pretty well”. With her coloring, she is NOT a Quarter Horse, so her short rump length could be bred in.
I am an App fan, and do NOT want them to be spotted QHs. They were not that way originally, still did an EXCELLENT job out running the Cavalry when asked! So good the white guys took away the Indian"s horses after surrender and bred the mares to ^#^ stallions to ruin the breed.
I know a lot of shorter rumped horses that do great jobs as working horses, in a great many catagories, so have learned not to “look down” on it as a fault. European breeds and WBs often have a short rump, still manage to do a fine job for their owners in various disciplines.
Western horses are judged on abilities, with some comformational areas making them better at some things than others. The most emphasized areas might be great ring winning things to have in their build, but not so good to be as useful on an 8 hour day across the ranch. There are lines of horses that are terrible gaited, you walk like a cripple after a few hours on that animal. You would never notice that problem in use only when ring riding.
With more training your horse can be a BETTER competitor, skill can overcome some lesser conformation points on an animal. But for an all-rounder as you listed your desired uses for the horse, she looks quite capable of doing all of them with moderate skills. She is not bred to be a specialist, reiner, roper, jumper. You probably won’t be last if she is well trained, though you may not be first often. But you only need one good horse, take her anyplace and have a VERY GOOD TIME using her.