Help with cat my husband feeds

I am new to this sub because most of my life, I didn’t care for cats. This was mostly because I am extremely allergic to most of them. My husband and I are dog people and have been for the last twenty years.

Fast forward to about two years ago. My husband was noticing this gray cat coming around and he would feed it from time to time I thought it was just a passing fancy so I don’t say much about it. Well, over time he grew to really love that cat. He bought him a heated house for the winter (we live in ny) which he’s never used and feeds him only the best cat food.

Now that she has gotten so comfortable, she’s decided she likes me. I’ve grown fond of her but absolutely can’t have her in the house between my allergies and my 3 dogs.

Here’s my problem. We plan to move early next year and I’m not sure what to do about her. Any advice?