D.M.
YES, YES, YES!! Contact the Dept of Child Support Services for an application and information.
What I recommend is even getting a consultation with an attorney...those are usually free and ask what your options are.
I got child support for my son when he was a baby and was custodial parent (Dad never saw baby) and still am. But since then, my son's Dad challenged that and we now have a visitation order that outlines a few days where my son sees his Dad for a few hours. Oh, and we were never married either. The thing you have to be careful about is creating tension and anger. I spoke with my son's Dad before I called and applied for the child support because he was giving me money in the form of checks here and there, and I wanted it to be on the record. So, he knew it was happening. You might want to inform you ex- that you're going to be seeking it...if you have that kind of relationship.
Also, be advised that as her father, he does have the right to be apart of decision making and things of that nature...so, if you are not friendly and he decides if he's going to pay support he also wants to see his daughter on a regular schedule this might come about as well, like with my son's Dad. We have Joint Legal Custody and I Have Physical Custody of our son now.
There are services like mediation and court aid offices that offer advice for no fees or minimal fees that can assist with understanding the process.
Definitely, get some professional advice, and depending on your relationship with you ex- you may want to talk about it with him and see how he feels about helping.
My friend and her ex- were able to get an agreement without legal stuff (going to court) and they both went to the Child Support office together...but, before that he just paid her monthly and they had a contract written up and signed by a notary. But, now that she's getting remarried they both wanted something in writing about visitation and child support. It can be amicable or not, just about to the two adults and how they choose to go about it.
Good luck and let me know if you ever need a chat!