M.S.
First of all she is not too young to discipline. Discipline begins as soon as your child is doing something they shouldn't be. You use a deep stern voice and say, "NO!" and redirect their hands or whatever it is that they're doing that they shouldn't be. Or if you are comfortable you can flick their fingers, not too hard, but enough to startle them to associate that little bit of pain with the bad behavior. In the same way you can teach a child not to bite you while nursing. When my son first started biting, even before he had teeth I would flick his cheek and tell him no, and he doesn't do it any more and has several teeth (10 months). It also sounds to me like she's not getting enough sleep during the day. Those behaviors sound like a baby who is overtired. She is pretty young to only be sleeping two hours during the day. "Healthy Sleep Habits Happy Child" is a pretty good resource for a book on children's sleep. Things that the author recommends are earlier bedtime (6-8 pm) and naps after the child has been awake for 2 hours. So she might just need a third nap during the day. Sometimes when my son wakes up early and his nap schedule gets moved up, he needs just one more short nap later in the afternoon to help him make it till bedtime. But no matter how late I try to keep him up in attempt to get him to sleep later in the morning, he wakes up like clockwork between 7-7:30 am. SO it's more beneficial to get him to sleep by 7 in the evening so he'll get more sleep. Email me if you have other questions. I by no means have the market cornered on baby sleep...but I have found a few things that work for my son. But be firm on the behavior and what you expect of her. Even if you don't use physical discipline, you can use your voice and your actions to teach her what is appropriate. Good luck!
Also, if you are comfortable nursing on demand, continue to do that. Even though they don't need nutrients, nursing is such a comfort when they're teething...but not in the night. Decide when you're going to go in, for instance once in the middle of the night and then not until morning (that's what I do) and if she cries before that time, don't go in, and if she cries after that time but before morning, don't go in. She will learn to comfort herself. I've just started putting several pacifiers in my son's crib so he always has one close. She is old enough to learn to get back to sleep. UNLESS you're comfortable having her in bed with you. That way she can nurse throughout the night and be comforted and you can both get some sleep. This worked with my son, but only until he was about 5-6 months old (which was sad we wanted him to stay in bed much longer) then we had to move him out of our bed and start sleep training, so the concept was new to me.
Missy