I don't have a lot of experience in barrels... I had a good barrel horse in high school but my focus was on the pleasure, so I only did a few years of it. So in my very unprofessional opinion....
If I'm reading this right, she's not loping at all? Or just not loping patterns? If she's not loping at all, there's no reason why you can't get that horse in gear and get her moving. In my opinion a horse should be loping within the first few rides. Some like to take it slow and go months of walking and trotting, but I get mine loping within the first few rides.
Loping a pattern though, needs to be done carefully and after they're done growing. There's a reason you don't see good barrel horses until they're about 8 years old; most haven't even seen a barrel until they're 5. It's a tough job they have and their joints don't fair too well if they're pushed before they're done growing. Just because she may look fully developed at 3, trust me, she's got more growing to do.
I think she probably needs a year as it is to get the basics down anyways. She needs to be BROKE before you venture into the barrels. I mean: moving off your legs, soft mouth, soft sides, taking cues, lead changes (simple is a must, flying lead changes are preferred). As of right now, as a 3 year old that doesn't lope, she certainly should not be getting into barrel patterns for quite a while. So there's my 2 cents. :) Good luck to you with your search!