Extension determines black (Ee/EE means black; that's why bay horses have black legs/points). Agouti is the red gene. It's why horses without it who have extension are black (have no red hair)
Fantasy, she's a bay with cream, making her buckskin. A horse with "aan" is only black if they have extension (Ee or EE), otherwise they'll be chestnut
Ccr is the creme gene,without it the filly would be bay dun. She has one red based gene (e) so she can give bay foals as well as chestnut foals (or even black ones since she's Aa)