Yea, dump that partner. It's your life they don't control you. Or stay with them and don't get a dog. You will eventually resent them anyway over it. I know I did, waited almost a decade to get a dog. When the answer was still "it's not a good time", I left and took my bank account with me.
Cruel irony after I left partner bought a puppy because he was lonely. Go figure, I think he just wanted all the attention. We don't talk. I have nothing to do with him. 10 years I'm over it.
Got a new life new lover and two doggies