Yes, but it is fairly rare. Most kids and adults have been vaccinated against it.
If you are breastfeeding and were vaccinated, the chance of your child getting it is low.
That's one of the vax my son didn't get...they didn't offer it as a single vax, so we chose not to do it.
That being said, if your 2 month old shows any sign of illness and isn't eating, pooping or peeing well, then off they go to the ped.
From what I understand, many cases of german measles go unnoticed in kids. It is most dangerous to fetuses and the very infirm.