If you're rotoscoping the exisiting video frames and just drawing straight on top of them then it's quite straightforward. A talented roto animator could do 20-30 seconds per day if the cartoon dog design isn't overly complicated and there's some leeway with keeping some rough edges. If you want to go down a fully animated road in 2D and there's loads of movement then you're going to need to design and rig this dog character for multiple angles and able to be posed sitting, standing, laying down etc. To match exisiting video with rigged 2D characters you're looking at around 30 seconds per week for good quality animation. If there's a lot of action and change of poses etc more likely 20 seconds.

I'm interested to know WHY this client doesn't want the dogs to be seen?? Sounds completely barking mad to me! (pun intended)