I have read this and I really feel for you. You made a mistake, you're human, it happens and, as a pp said, it's what you do after that matters.
I absolutely cannot believe that there are people on here telling you to live a life of deception and just not say anything to your DP and not take a DNA test....what on earth are they thinking?? These things have a horrible way of crawling out of the woodwork when you least expect it and, from bitter experience, the longer it's left the bigger the repercussions. Of course hindsight is a wonderful thing and you would have fessed up at the start but I absolutely understand why you didn't.
I'm not sure how it would work if you had a test without your DP knowing, what would you say if it came back as him not being the father? Realistically it's not going to work, you need to be open about it.
Let the dust settle, let the excitement die down, let you recover physically and emotionally after the cs and then think again but please, don't do what pp have suggested and just ignore the issue indefinitely (FWIW you sound lovely and I don't, for a second, think that you would) as it's unfair on you, your DP and your beautiful baby girl.
Good luck halle, I hope you stay kind to yourself 