Booster jab

Did anyone take their booster near their EDD? How was it? I'm week 38 now and baby is quite low already, my first 2 were Pfizer. My gynae suggested I take Pfizer so baby can get some antibodies over the remaining week(s), and said that transfer of antibodies is lower through breastmilk. Wondering if I should take it coz my baby is quite low already and it seems like I'm losing my mucus plug. Thanks!!