How to I change from no dog to has one dog on my profile?

Since your profile isn't active yet (i.e., Rover hasn't approved yet), I would wait until it is live to make sure that it has that info. From what I can see now, your dog shows up. So long as it shows up here:

https://www.rover.com/provider-profile/…

then it should be reflected on the profile potential clients see. If not, then check with Rover Customer Support to find out why it isn't carrying over.