J.S.
If it were me, I'd wait.
When I was pregnant with my first, I got a job interview out of the blue (had sent them my resume a few months earlier) at an office that was 10 minutes from my home. At some point in the interview (I really liked the HR person and the office), I told her that I was pregnant and didn't feel comfortable keeping that information from her. I also said that I'd like to wait until after the baby was born before moving to another company because of the maternity benefits. She really appreciated my honesty and I promised to give her a call after the baby was born to see if they had anything available. Low and behold, they did need a part time person. I ended up working there part-time for 5 years. I quit after my 3rd was born.
This was over 14 yrs ago and times have changed considerably - especially where benefits are concerned.