Kylie - congrats on the new job!
One of the girls at work was going through contract negotiation when she first found out she was pregnant. Even though she has been at work for over a year, she decided NOT to tell work until her contract was finalised. When she announced her pregnancy, she was about 16 weeks. I work in health care and our work environment is potentially very violent (drug and alcohol clinic) and chose to tell my supervisor and boss at about 8 weeks but didn't make it public until I was about 17 weeks (I went off on holidays before I hit 12 weeks and didn't want to say anything until after 12 weeks). I had no problems and they were very excited for me - even though at my work these things come in 3's and the other two pregnant women are both from my department! The third girl wasn't going to say anything until she hit the 12 week mark but began to show (rather noticeably) at about 8 weeks and felt she couldn't hide it anymore.
My advice is that you need to do what you feel comfortable with. For me it would depend on the kind of work you are going to be doing in this new role. I know you said it is research but it depends on what is involved for you. If you are concerned about your job security, they can not do anything if you have already signed your contract. Also, it seems that you have been at that hospital for over a year so your maternity leave entitlements should all still be in tact (but check with HR if you're worried).

HTH and good luck with your decision. Congrats again on the pregnancy and new job!

MG