Start slow and don't over do it. Watch that ligament closely so you don't aggrivate it and set yourself back.
I would start with just a short ride a day at a walk. You should be able to notice when she is ready to go further, keep it at a walk for a couple weeks.(maybe longer depending on her condition and how much she improves) This will just help to build up a little endurance, then increase the workout gradually.
Quick speed is very important for a barrel horse, but in my opinion endurance ranks up there too. Sure you can have a lightning fast horse but if she can only keep that top speed for half the pattern, then that speed doesn't do you alot of good. To judge if she is at the right level of endurance, see how hard she is breathing after you run the pattern. Yeah she will probably be breathing hard but how hard is the key. If she is really struggling you need to go back and work on her endurance. Get that squared away first, then work on her quickness. One of the best ways I have found to increase sprinting speed is to start standing still, bring her to her top speed in as short a distinace as you can, once she gets to top speed, stop, turn 180 degress, and go back to top speed (all in one motion), hopefully she will reach top speed in a shorter distance, stop, turn 180 degress, back to top speed.Try to stay in a straight line soshe has to turn 180 degress, this will make her work her hind end. The key is to get her to go from 0 to top speed as fast as she can each time doing it in a shorter distance. Don't over do it! I also drag a log if they allow me to to build up muscle but for a speed horse too much muscle is not always a good thing.
There are many many ways to get a horse into shape and I'm sure others on here will give you really good advice, but nobody on here can tell you exactly what is best for your horse, you have to judge that, all we can do is give suggestions. good luck.