You shouldn't feel guilty. My bet is you feel guilty for 1 (or a combination of) the following reasons (humor, but some seriousness, intended):
1. You have been raised to be a people pleaser (probably since you were little - take a look at your family dynamic and your history of past relationships); which means that you avoid conflict, you take on more accountability than you are entitled to, and you probably have some co-dependency traits. So you feel that by taking his money it means you aren't doing "enough" to provide for your child. So, in your mind, it makes you a "not good enough" mom.
2. Ex is a loser; bordering on (or actually is) abusive. Abusers like to make their victims feel like they are simultaneously undeserving and responsible at the same time, while going great lengths to get off scot-free themselves. (review the traits of #1 - these go together like ramalamadama).
3. You trapped him into impregnating you even though he brought condoms and faithfully used them every time (but you poked had a million holes into them and made sure you had sex when you would conceive) in addition to you lying and telling him you were on the pill and didn't want to get pregnant. Your relationship was bad and he was ready to break up with you, when you convinced him to have sex with you in order to trap him. So the guilt is actually something you should feel.
4. As a society we have ingrained into women that we are the caretakers of our children. We routinely let dad (not all - I am NOT dad bashing... my hubby is FANTASTIC with our kids) get off with doing "less" and we accept dads that don't pay child support or actively engage with their kids. This is because historically their "job" was to provide an income and so we tend to still see them in this role. We *take on* more child rearing tasks than we should which doesn't give dads an opportunity to dad-up and get involved.
5. Society has historically painted women as "gold-diggers". So you don't want to be seen as "going after his money". If it makes you feel better.... open a 2nd checking account where ONLY the child support goes. Then use the child support to pay for things only for your daughter. Buy her clothes from that account. Any extracuricular activities, school supplies etc. First of all you will soon see that you are spending more than that account on your daughter. 2nd you can "justify" (if even only to yourself) what you are spending "his" money on.... although you don't HAVE to justify. To ANYONE.
Just a few thoughts on a Tuesday evening.
For what it's worth- you are really going to have to stay on top of Domestic Relations. they can move at a SNAIL's pace if you aren't calling them and checking in. You are the advocate for you. You are the advocate for your daughter.
FWIW#2 - guilt and fairness are the evil twins of justice and equality. OF COURSE he should pay child support. It's extra crappy of him that he MADE you take legal action.