This horse is not blessed with great conformation (but I bet she has a great disposition!). Her neck is short and poorly placed which will make it difficult for her to roll back onto hind legs and shift her weight to the rear to slow for turns or to change leads with a rider on her back. Her back is stiff looking and too straight into a peaked and steep croup. She is stiff looking through the barrel.
Her hind legs are sickle hocked. This is partly due to how her entire hindquarter is built with the high peak and steep croup. The stiffness in her back is likely due to the straightness of it and the sickled hocks. Of course, if she is stiff in the back, the standing under herself will help take pressure off her back.
This horse needs caveletti work and hills.. trotting up hills with a loose rein and your weight in the stirrups and forward off her back. This will build her "ring of Muscles" that support the entire hourse during athletic endeavors INCLUDING trail riding.
She is not physically ready for barrel racing at all. She needs lots of circles, spirals in and out, caveletti, serpentines and practice at changing speed IN a gait and BETWEEN gaits. When you can get smooth transitions.. extension and collections IN a gait (trot) and smooth transisitons without head tossing or resistance between gaits (trot to walk, Walk to trot, walk to halt, trot to halt first then canter.. trot to canter, walk to canter, canter to trot and canter to walk) you can then start Barrel training. I would not expect a stellar performance but you will learn a HUGE amount in the process.