The first time DW and I went to WDW (her first time ever) she was about three months pregnant with our second DS. Our first was about 2-1/2. It was February so not really hot, and since it wasn't crowded, we let him do a good bit of walking and travelled at his speed, so not as tiring for her. Other times we pushed him in a stroller. She didn't ride very much.
Then when our second DS was about 4, we made plans for a big trip back to WDW since they were both old enough to really enjoy it. I had travelled a lot and we cashed in Frequent Flyer miles so we all had a free round trip ticket. We booked the flights and reservations well ahead of time, and lo and behold just before we got ready to leave, she finds out she's pregnant with DS number three. She once again decided to skip a number of rides for safety's sake, and it was around June/July so much hotter, but not too far along yet to make it too miserable for her (except the disappointment of once again missing all the fun rides since she is a roller coaster type girl).
Well, our DS number three had reminded us for a while that he had never been to disney (even though we kept reminding him he had, he just couldn't see anything at the time) but life kept keeping us from planning it until he was ten last year. Since our oldest was about to go off to college, we decided it was time for us all to go while we still could. And for those who think they know where this is going, no, we didn't find out she was pregnant this time, and she finally got to enjoy the whole Disney experience this time around.
As some have said, everyone's situation is different. The best advice I can give you is to listen to your body when it tells you to slow down or take a break. Be smart about it. If you don't get to do it all this trip, it just gives you an excuse to go again in the future. I always enjoyed going to DW when I was a boy, and even as a grown adult, but it is great to watch the wonder and excitement in your child's eyes when they get to experience it, especially for the first time.
As for rides, I can't imagine Pirates of the Caribbean being too much for you, depending on how far along you may be. It only has like the one short drop that I remember. And I really can't imagine Kali River Rapids being too much. We did that for the first time this past year and I thought it was the lamest river rapid ride I had ever been on. As for Mission Space, there were two lines for that ride....one with the full motion experience, and one that I believe lets you "see" what is happening without all the movement, which they recommend for people who may have motion sickness problems or heart conditions. I never saw what that one was like, but at least check it out and see if pregnant falls into the other categories where you can still do that one. Other's on here may have done the milder version and can comment.
Things like rock 'n roller coaster, test track, tower of terror, splash mountain, space mountain, etc. are definitely ones to avoid. Head the warnings if you have any doubt at all. Like I said, trust your instincts and what your body is telling you. If you have any question or just plain don't feel right about it, err on the conservative side.