You don't need your horse cranked into a perfect headset, or doing dressage stuff to be collected, if fact, headset has nothing to do with collection, but if you get them really driving with her hindquarters, they will most likely round up throughout their whole body, resulting in a nice little headset.
Now, the collection we use barrel racing is much different than dressage or reining. Reining/dressage horses are supposed to be nicely rounded and collected consistently. Barrel racers really don't want that, we would like it practising w/t/l at home, but mostly, we want it when we ask for it to get a horse really working around a barrel or doing a lead change at home, or working some issues out. But when it comes to actually running the barrels, the collection work really comes into play when you ask for that rate and the horse starts driving around that barrel and you can feel their hindquarters really working, instead of flying around the barrel all uncoordinated-like.
If your looking for exercises to do for barrels, there's a lot of videos and reading here: Barrel Racing Exercises and Drills.