Start training her in basic dressage. Basic dressage, like basic reining training, helps any horse be a better horse no matter what direction you end up going. Having control over all parts of a horse's body, having control over speed and collection and having control of a horse's mind will make him more successful at whatever he ultimately trained to do.
Additionally, one can turn a horse with a dressage background into a barrel racing horse a lot better than you can take a barrel horse and turn him into a dressage horse.
Another thing to think about is even if you do not want a dressage horse, if he really takes to it (you can't lose with free training if the trainer is any good), you could probably sell him for a lot of money and buy a really good barrel horse with the money. I do not see how you could lose by at least starting him in dressage.