I have a 3 yr old, 18 mo old, and 3 mo old AND 2 dogs and a cat. I think what you are experiencing with your 20 mo old is very normal. She is experimenting with cause and effect and enjoying the new freedom she has now that she can walk and explore. Obviously it is not OK for her to hit the dogs - both for your pet's safety and for hers. I would keep the 2 separated by gates / lock your pets in another area of the house if you are not in the same room watching them. It is important for them to still be around each other, but with your supervision so you are right on top of her if she is too rough.
Sounds like you have already done the "too rough... be GENTLE... GENTLE" reminders. Next I said "be GENTLE or doggies go bye bye" and if my son hit again, I would put the dogs away (with treats and good-boy pats to the dogs). No big production. Hit = No pets. Then told my son "You can only be with dogs if you are gentle". Later I used time-outs for reinforcement but she may be a little young for that. She is still your sweet, kind little girl. She is just curious and exploring and it is poor mommy's job to figure out a way to teach her what is appropriate. Every child is unique. Try to figure out what motivates her. Also, I try to have their time when they are with the pets when they are not sleepy. They listen better and tend to be more patient, gentle, and caring when they are rested.
Is she looking at you when she goes to hit? It may not be the hit that she is interested in, but more your response and or your attention. My 18 month old has figured out how to move the gate that blocks our stairs and he has no interest in going upstairs but loves going up a couple and waiting for me to chase him. I try to think of it not as disobeying but his way of saying I want/need attention. Frustrating for me though. Being a mom is such a CONSTANT job.
Good luck! Give that cutie a big huge!