I'd recommend to wait until after pregnancy/nursing to perform any elective cosmetic procedures. Pigment production is increased in pregnancy (the mask of pregnancy or melasma) and any extra inflammation could rev up more pigment. Also, certain chemicals used in peels, such as salicylic acid, are not recommended during pregnancy/nursing because of unknown effects on the baby.
I would not recommend chemical peels for pregnant women. Although systemic absorption of chemical peeling agents is low, it is not zero. Microdermabrasion itself is likely safe, but other topicals frequently used in association with microdermabrasion are not recommended, so you would probably be better off delaying microdermabrasion as well. Hypothetically if something were to go wrong with your pregnancy (related to a cosmetic procedure or not), you would not want to be in the position of second-guessing your decision.Good luck.