I'm not sure what the effects could be on that type of shot so I really have no input onto that but I do want to say wait just in case, to be safe!
I would honestly wait untill after the last date that you were told just to be safe.
Better safe than sorry!
Because you have plently of years to come to enjoy your life with your child and no need rushing these things especially if speeding up the process could possibly effect your child and that would be hard to live with.
But the decision is yours to make.
When I found out I was pregnant I went to my dr and he ran some blood work. Included was a rubella immunity, according to that I am NOT immune to rubella. My dr's EXACT words to me were "IF YOU SEE/KNOW SOMEONE WITH RUBELLA, RUN THE OTHER WAY!!"
If I were you I would wait 2-3 months like your dr told you. I have no idea the effects of it on a fetus but it must be bad if my dr told me that I should run the other way. I will be getting a rubella shot right after this baby is born. Probably before I even leave the hospital.