She's cute. The pictures aren't critique worthy. I'd wait on barrels until her joints have matured. Barrels puts a lot of stress on the leg joints and the last thing you want is for her to be unserviceable at an early age
She is cute, but I have seen better looking youngsters. I wouldnt put her in my barn, and that's just me. I have nothing against Tennessee Walkers, I have rode pleany of them and know them personally. Please, don't ride her hard until she is at least four. She is young, and still a baby...
When starting a horse for barrels, it needs to be done slow and easy. Defiantly not at two years old. I have a three year old mare that has not even ran the pattern yet. Groundwork is just as important as riding. If you start too soon, you are only hurting yourself by having to step backwards later to fix problems that have occurred. Babies need time to grow and be babies, I believe this to be true for all horses but especially for barrel horses.
Shes very cute that's for sure. I think its fine to start training some horses at two, not all but some. I do think barrels should wait until she's about four or four and a half. Make sure she has all the ground work she needs and be able to understand everything clearly. Theres alot involved with barrel racing besides the pattern. For a horse that doesnt know simple things like lateral/vertical flexion or leads it makes barrel racing down right difficult for the horse and the horse will learn to hate it. For the next year or so just keep riding and doing basic drills. Don't push her. I also think you can ride a two old more often than once a month or twice a month. Her almost three you can definitely get up in the saddle anytime you like. Just don't make it hard.