I’m at the start of season 4 and things may change later on but at present the army of House Targaryen consists of a hoplite army of freed slaves. They are in vaguely Ancient Greek / Macedonian-style outfits that are completely black, including black shields and helmets. The other armies look more like 100 Years War / Wars of the Roses armies (but they are on a different continent to the Targaryens).
Just to complicate things, in season 1, the Targaryen army was basically like a Mongol horde and solely consisted of cavalry. And I have the feeling that if the Targaryens do cross the sea to fight the other Houses then the nature of their army may change again.
You might need to bite the bullet and watch the series to find out what your daughter wants. I didn’t think I was going to enjoy it but so far it has been as good as everyone says.
I haven’t seen any Impetus army lists but there are a few for Hordes of Things on the internet.