Sorry this is so long.... :)
I think this is something you should definitely bring up to your doctor at your next appointment. I had a lot of anxiety (not about caring for DD, but other reasons, I won't mention because I don't want you to take on my reasons as well). I gave myself until 4 months to work it out on my own, and then I had to get help. It took me another few months to get the courage to go.
I've seen a counsellor 1x/month for 3 months and I feel a lot better and am going to stop going (with her blessing) unless something else comes up. I just needed some tools to help me understand what is happening.
I'll give you a run-down of my "questions" to ask myself
1.) What is happening to me physically - am I pulling away, is my heart racing, am I sweating?
-> This is going to help you identify it before it starts
2.) What am I thinking - sometimes you have to force yourself into what you are thinking and find out what you are actually saying to yourself.
-> What am I saying to myself?
-> Is it true?
-> What would be a "more true" statement?
-> Is it helpful?
-> What would be a "more helpful" statement.
"I feel like I can't take care of her?"
is it true -> No
what is more true -> I have been taking care of her for 5 weeks. She is fed and clothed and happy. I am meeting all of her needs.
is it helpful -> No
what is more helpful -> I am feeling this anxiety because I want her to have the best always. There will be things I can not fix, but I can help her through anything that does go wrong. I have done this so far by kissing and hugging her. Feeding her and soothing her.