So here's what I THINK I know:
Since black is dominant, and red is recessive, she is Ee.
Since agouti is dominant, but doesn't affect red coats, she is either Aa or aa.
But I'm not sure how the brown gene works, so she could be At?
She has a 2yr. Old bay half brother, whose sire is listed as black on allbreedpedigree. You can see a picture here: Man With The Power Appaloosa
This is soooo confusing
ETA: The picture is of the 2yr. Old's sire.