Yes, it is new. Go and get one. 
Firstly, moving in April will give you loads of time, and will be a great time for it as you'll be in your second trimester and will have a lot more energy than you do now.
Secondly, going to New York will be exactly what you need. This will be your last opportunity for a long time to go and enjoy yourself and your DH without being knackered and otherwise occupied. There will hardly be any jetlag involved with it being New York, and it will be brilliant. Don't worry about that.
Thirdly, just get yourself booked in with a midwife where you are and don't worry about changing. You might even be glad of a change when it comes to it, midwives can be a real pain!
Now let me tell you about our move.
We bought a house that needed total renovation about 250 miles away from where we were.
I was pregnant with twins, and had SPD, so took maternity leave as soon as I could, at 29 weeks. (Teacher, so quite physically tiring work).
We moved to near where the house is, to a friend's house.
I spent the next 2 weeks decorating and organising builders (tricky, with SPD and so heavily pregnant with twins to paint walls etc.) I registered with the doctor and midwife straight away, and they both saw me within a day or two.
At 32 weeks we had a scan that showed one of our babies had very sadly died. In that night for emergency CS the next day. 1 week in hospital for us (luckily they let DH stay as there was a bereaved parents room), DD still in NICU but we had to leave. Not emotionally ready to go back to friend's house, plus she didn't want the baby there when she came out (2 dogs, not the cleanest of houses). So, we left hospital, found a hotel (took a couple of hours, felt very Mary and Joseph!) for the first night. Went to Tesco and bought a steriliser (hospital lent us a breast pump, as DD was too little to feed without a tube).
Found a holiday cottage to rent, kept going to hospital a few times a day to hold DD, friends came to stay in cottage too (male friend fitted kitchen). Stayed for a week, then went back into hospital with DD to learn how to feed her. DH slept on the floor of our unfinished house (still no kitchen) as no more money for holiday cottage.
When we left hospital, another friend agreed to let us have her spare room (cleaner house, no pets, DD still very tiny and fragile). DH used his paternity leave and called in favours from all kinds of friends and family to get the house habitable. A couple of weeks later the furniture arrived and we moved in. House (19 months on!) still isn't finished, but is habitable.
My point here isn't to scare you, but to show you that, even of the worst does happen, you will get through it. Although it would have been lovely for the house to be finished and be all settled before coming home with a baby, it really was the least of my worries, and just seemed like a minor inconvenience, with arranging the funeral and everything else that comes with having a newborn and grieving.
Do what you have to do. It may not be perfect, but it will be fine. A move in April will give you plenty of time to get everything sorted and it will be lovely to have a new home for your new baby. Neighbours will be more friendly if they know you are expecting, which is a lovely way to start in a new area.
Good luck, don't worry, have a
and enjoy New York (you lucky thing!