No - the MMR vaccine is a live attenuated vaccine, so it’s not advised during pregnancy. Women planning pregnancy should ensure they are vaccinated at least one month before conceiving, and family members and caregivers can check their vaccination status and be brought up to date to protect them. If a pregnant woman is not immune, she’ll be advised to get vaccinated after delivery.
MMR vaccination can be given safely to a mum who is breast feeding, without any risk to their baby.