Your baby's hair sounds very similar to mine: very curly but very thin, with lots of ringlets.
She also does play with it a lot and tell me about that spot on the back (sigh)!!!! Her hair right now is kind of short (neck length) so it's easier to care for. I do the same thing that you do except that I use a little bit of coconut oil after the leave-in conditioner to keep the curls defined (until she messes them up ). But I also use headbands and cute hair pins, you can do so many styles with babies and curly hair and it looks great on her even with a frizzy hair. Just pull some curls together and throw a pin in there.
Sorry about the haircut experience but, I think at this age, the look doesn't matter, your daughter is just a baby I'm sure she looks cute even with a messy hair. The important thing is that you are taking care of her hair and your keeping it healthy for her until she grows a little older.
A Mediterranean 3b lady
In love with my curls, love love love
CG since Nov/07

Co-Wash: VO5, Tresemme naturals, Fructis naturals
Cond: Nature's Gate conditioners
Stylers: Lotions made at home with coconut oil, honey, AVG, vegetable glycerin, OO, and EO.
Gel: LA Looks sports gel for high humidity days.

Hair goal: Waist length healthy curls