Absolutely not an expert on this, but doesn't your daughter get the immune antibodies from her mother in the first few months? Either passed during pregnancy or by breastfeeding.
I'm not actually sure why they vaccinate for MMR at one year as opposed to earlier like other vaccines. There must be a good reason.
https://www.who.int/vaccine_safety/initiative/detection/immu...
[1] Except when they're broken, and then it sucks bad, and you find out how damn amazing they are and how much we take them for granted.
You can receive a first MMR dose earlier than 12 mos for certain grounds (e.g. international travel, military postings) but it is then recommended that the infant receive a second 'first dose' after 12 months.
Also, it is a relativly recent development that adult humans can even digest milk. Lactose tolerence is the mutation, and a sizable portion of humans do not have it.