There are a few rides that do have advisories for pregnant women and guests with heart or back problems. These are typically the thrill rides like roller coasters that have sudden stops, rough motion, or lots of spinning. These advisories are well marked on the park maps and on signs outside the attractions. This information is also noted on the attraction pages on the WDW website. For example, scroll to the bottom of this page about
Test Track, and you'll see the advisory. By far the best thing for you to do would be to speak with your personal physician about your plans and get his or her advice on the types of attractions you may want to avoid.
I visited WDW when I was five months pregnant with my twins. I was huge
and uncomfortable, but I had a great vacation. I was able to go on lots
of gentle rides with my older daughter (who was 2 1/2 at the time). In addition to that, I took
full advantage of the numerous shows, parades, fireworks,
character greetings, dining, and other experiences that involved only
sitting. In my opinion, it's worth the price of admission just to see
all the wonderful architecture and atmospheric themeing. I also had a
great time at my WDW hotel pool. The buoyancy of the water really help
take the strain off my back.
Congratulations on your new addition to the family. I hope you all have a wonderful visit to WDW.