First thing first, get a dog that doesn't shed, theres alot of them...
Now if you really want a dog theres a lot of ways to persuade her to let you have it, It gives you responsibility, it lightens you up and puts you in a better mood, which again reflects on the energy in the house.
You get training because the dog will motivate you to go out and have a great time with it, the list goes on...
I can't see what she wont let you have it, theres too many positive sides to it....