MMR vaccine for breastfeeding mom

I have low immunity to measles and consider taking MMR vaccine. However, I am breastfeeding a 12 week old baby. Is there any chance that the live attenuated virus can pass through breastmilk? Is there a significant amount of antibodies can pass through breastmilk? I am weighing the options and risks to make decision.

I have read these

https://www.cdc.gov/breastfeeding/breastfeeding-special-circumstances/vaccinations-medications-drugs/vaccinations.html#:~:text=*%20Influenza.%20*%20Measles%2C%20Mumps%2C%20Rubella%20(MMR),(VZV)%20*%20Typhoid%20(Ty21a)%20*%20Monkeypox/Smallpox%20(JYNNEOS)

https://www.ncbi.nlm.nih.gov/books/NBK501687/