I've been living with a woman for three years (Florida) and we have a 2 year old daughter. We're not married and I've never refered to her as such. If we separtate, will I owe alimony or any type of support other than child support?
Alimony is not an issue if you have not been married. Florida does not recognize common law marriage. Even if it were an issue, with a 3 year relationship, there is a presumption against permanent alimony.
As you noted, you and the mom will both be responsible for supporting your child, no matter what the state of your relationship is.