There is a thread for this, but anyways... is it one of these?
Tsukuyomi: Moon Phase
Zero no Tsukaima
One has vampires, the other has 'zero' in the title, and both have a little girl as the leading female.
Wait, maybe you mean
Karin. Also vampires, but the little girl more fits your description, even though she's a minor character. (for some reason i was thinking you were refering to the lead)