How do I add doggie day care on my profile?

To clarify - you have already completed the following steps:

Go to Profile - Dog Boarding Profile - Services and Rates - and then to the itemized choices

I don't see Dog Day Care on my profile, either!

True. There are many threads on the Q&A board about day care and the many sitters who want to offer it.

Rover recently added Dog Day Care as a filter, which seems to indicate that this additional enhancement to services is in progress.

For now, the best place to provide dog day care rates is adding it to profile text. (Unless you don't offer walking services and want to use that box for a day care rate)