One of my friends who shot a guy's eye out with his BB gun said he'd never give his kid one - he'd go straight to .22s because kids _will_ play with BB guns but not with .22s. shrug - I see no reason to divide up the training. No reason she can't shoot a gun, throw a rock, and learn a bow and arrow at the same time.
If your daughter has expressed an interest in marksmanship, start with what she's interested in and see how long it lasts. At 10, it may be 15 minutes, then on to violin.