Tricky one, ideally baby should be seeing daddy but of course its going to depend on each situation hun.
If you can come to an agreement with him about seeing baby then that's better than him taking you to court for access which he could realistically do .
There is no reason why baby can't go out, so it would be down to you & how you feel on it hun. He will have to understand if you feel uncomfortable just yet coz frankly so would i, but you also have to understand he is the babies father & is also entitled to see baby without you if you are not together. He also needs to provide for your lo, so this will need to be brought up ie either payments towards her or he should buy what she needs & give it to you.
Best thing if you can is to be as amicable as possible that way it would be easier to say you are not ready to be seperated from baby just yet, maybe ask if he wants to visit baby at your place, or tell him if he wants to see baby to ring you in advance 1st & then you can both agree a time & place if elsewhere.
The more amicable you are the better & easier it will be for you.