How about "Puter", so when she is out and you want to call her you would shout "Come-puter".computer.
Or how about "Arf". So when you are calling her you would be shouting ARF!, Arf! arf!
I know they are old jokes. Here are a few that sound close to "minnie".
Bonnie, Angie, Annie, Brownie and Aggie. I like Bonnie.
Adrien