I had my belly button pierced when I became pregnant. I bought one of the pregnancy rings and it worked fantastic. It was a clean sort of plastic ring and it conforms to your stomach to keep your piercing from stretching or closing. I wore it all through my pregnancy and labor. After I had my son I switched back to a regular ring but I have a lot of praise for the one I had during my pregnancy it never bothered me once. I was kind of indifferent like you but it was only I think $7 so I figured why not.
They sell pregant belly rings, they are longer. Personally, I'd take it out and just re-pierce if you want afterwards. If you end up with a C-section, it will need to come out. The amount of pulling and stretching they doctors do on the abdomen may end up ripping it.
I also had my belly button pierced when I became pregnant. I wore it all the through my pregnancy. I never took it and had no problems.The while did not stretch all.
Personally I would take it out as soon as you can. I wouldnt want to risk infection from (as you said) the stretching and pulling from the open hole. Take it out now and give it a chance to heal. I know a couple of people that have had no problems and a few that have had it get ripped so bad they cant get another piercing anyway. Its all up to you.