oomis,
I’m NOT a posek 🙂 but the GR”A held that a woman should NEVER enter a cemetery. Obviously the minhag is to be maikel.
Many Rabbonim say that a woman during certain times should not enter a cemetery.
This is obviously even when not pregnant.
I’ve never heard of a levaya being an issue.
BTW, R’ Webster mentions the zoo issue in Ch.15 Par.5a.