Is it safe to have mercury tooth fillings while pregnant?

Yes. The mercury is a non-issue. No evidence that it will harm you or the baby. That said, we try to get all dental work done in the second trimester. If you are having pain, that's another story. Rule of thumb though, get all your dental work done in the second trimester. Cleanings can be done at any time.
NO!!! Several countries including canada, germany, sweden & austria have banned or discouraged mercury fillings, esp. In children & pregnant women. Even our own fda now says "dental amalgams contain mercury, which may have neurotoxic effects on the nervous systems of developing children and fetuses" & cautions against mercury fillings during pregnancy. I don't think anyone should have mercury fillings.
IAOMT protocol. I would do it asap as you are constantly releasing mercury vapor. Use dentist who adheres to the iaomt protocol. Google it. I would start with googling for a holistic dentist as they are the most likely to follow such a protocol. You may also consider a heavy metal detox. Naturopaths are generally familiar with such things. And you can also google it. Avoid chelation therapy. Go naturally.
No. You want to limit your exposure to mercury in pregnancy, which is why there are only certain kinds of seafood that are safe to consume in pregnancy.