You sure don't want a perfomance horse type for barrel racing. You are very welcome. Our fastest time was 14.53 in barrels. In some ways the shorter horses can manuever and bend better than the big horses can. I'm sure you will enjoy it and please let me know how the search goes.
Horses are unpredictable.
If you are not experienced, handle horses under the supervision of a qualified instructor. This forum is not intended to be an instructional guide, and any one who uses it for this purpose, does so at their own risk.