I have gamed regularly with my 11-year old for the past year – as a dad here's my take:
Complexity-wise, Frostgrave should be easy for a 9-10 year old to handle. There are only a few stats to deal with and a little basic addition and subtraction.
As far as subject matter goes, there are some 'dark' aspects – necromancers, summoners and witches all have some occult elements that may not be suitable for kids. IMO, as the parent, that's strictly a matter of your judgement about what you feel your child can handle. Some monsters (zombies, skeletons, wraiths and similar) might also be disturbing for some kids. My kid likes beating up the undead, so no problems, but kids are all a bit different!
The only other aspect of Frostgrave that might be an issue for playing against your daughter is that a basic premise is competition between wizard characters and their retinues – the default game is your wizard against the other wizard. It would be possible to tweak the scenarios toward a dungeon-crawl format – her wizard against the monsters. I know that my kid generally prefers that format where dad runs the "bad guys".
As for alternative games, the one my kid and I have been using for the past year is 'Song of Blades and Heroes' by Ganesha Games. It also has very simple game mechanics and can easily be adapted to whatever setting your daughter likes. The figure-counts for warbands tend to be very similar.
Whichever rules you decide on, I hope you and your daughter have fun! I've found it really amazing seeing some of the different tactics my kid has cooked up (compared to the middle-aged guys I usually play against).