Very normal :). Congratulations!
You have a lot to deal with in the first trimester, psychologically (the uncertainty until you see that first scan, the idea that there is now another person you are totally responsible for, anxiety about what is to come during pregnancy and birth, etc) and physically (the hormones, nausea, tiredness etc, etc, etc - the list goes on!).
I think it is hard after you have been working towards the goal of ttc, to find you have acheived your goal, but you don't have anything to show for it yet (no scans, bump, baby, no-one knowing about it, etc). And now there is not much you can do to move things along but wait. If being pro-active about something would help, maybe look at how you can look after yourself the best you can during pregnancy, in terms of safe exercise, relaxation, nutritious pg friendly foods etc.
I am now 13 weeks pg with DC3. I have 2 lovely DDs, then had a mc in June, which convinced me even more that I really did want another baby. I have just had the most anxious 12 weeks of my life. Sometimes I felt nearly paralysed by how scared I was that something would go wrong, literally I would just be sitting on the sofa unable to think about or do anything other than worry (normally I'm not like that!). And even then, I had the odd moment of "have I done the right thing, can we cope with 3?". I think it is normal to have conflicted feelings, no matter how much you want the baby, especially early on in pregnancy. I also found that as I saw the scans, and as there started to be movements I could feel, that I felt more comfortable and more connected to the baby. I found it helped early on to tell a couple of close friends I was pg, so I could talk about things with them, and felt I had some support.
I also agree you should talk about this, whether that is with DP, your midwife, RL friends, or just us on here. The chances are you will feel better soon, but if you are feeling low for a prolonged period, do bring it up with your mw, as it is possible to develop antental depression. Just from experience of myself and mum friends, I think it's likely you will feel better as the pg goes on though :).