I understand that all attendees to various events need to show that they are fully vaccinated, but does that go for a 6 year old as well?

Yes, or a negative COVID test.

My granddaughter has only had one vax so far and they were fine with her one dose card

Yes

Negative covid test and usually they have rapid tests right there, like they had at the opera house.

Under 12 requires a negative COVID test.