This stuff is fun.
So she's questionable on Extension status but working on the assumption she's e/e (because she looks red to me), knowing she's A/A, and knowing she is at least D/d, if bred to an E/E stallion (any Agouti status, no extra modifiers), you would only get bay or bay dun. E/e would give you red, red dun, bay or bay dun. You cannot get a black or a black dun out of an A/A mare.
The only time you NEED to know exactly what genes your horse has is if you want to breed from them. That's why I think about colour genetics from a "what it can throw" perspective, because for most people that's how it's relevant. E/E can't throw red. A/A can't throw true black no matter the Extension status. A grey or a roan has to have at least one grey or roan parent. Silver and Agouti both hide on red, cream can hide on black.