Girlfriend (25f) called me (28m) unfair when I said I'd only be putting my name on the deed when I but a house?

I have been with my partner for over 3 years and we've said in the next 5 years it would be nice if we had enough for a deposit for a house. Last month I won a pretty substantial amount of money on a gameshow which will allow me to pay a large down payment on the house and get a mortgage.

I was talking about this with my partner and mentioned to her that since I would be the one paying the down payment and deposit that I would only be putting my name as a homeowner. I said I don't expect her to pay towards the mortgage, I'd only expect her to contribute towards utilities and groceries.

She said I was being unfair since we were planning to buy a house together. I said that if she wants to wait until we both have the money then that's fine, I'm more than happy to wait. She said since I have the money now, it makes sense for us to get a house now since it would mean we're not paying rent anymore.

I told her that's fine with me but if we choose the option to buy sooner then I will be the sole homeowner. She again said I was being unfair since it should be both of us but I just pointed out that I'm the one paying the deposit and down payment so I'm going to be the one who owns the house.

She just repeated that I was being unfair towards her and that we should both be on the deeds as homeowners. How would you handle this?

tl;dr I recently won a substantial amount of money. I planned to use the money for a deposit for a mortgage. I told my gf if I paid the entire down payment then I would be the only homeowner but I am more than happy to wait until she has her half of the deposit if she wanted to be co owners but she said I was being unfair and should put her name down on the deed anyway. How would you handle this?