AITA for not telling my stage 3 cancer father about my separation?

I’ve recently (about 7 months ago) got separated from my wife (although not legally yet) of 12 years. About a month ago I started seeing someone and hitting it off pretty well.

As we’re getting closer, naturally we started talking about our baggage to each other, to put it all out on the table. One of which, for me, is the fact that I haven’t told my father that my wife and I decided to separate. My dad has always been a “conservative family values” type of person, so one of my biggest concerns with the separation was how he would react. Then a few months ago he got diagnosed with with some type of Stage 3 cancer, and he is currently undergoing some sort of therapy treatment. He is not doing very well, telling me almost daily he just wants to die instead.

When I brought this up to this new person, she had a bit of a problem with that. She said if we were to get serious, it would be unfair (and just stupid) to have my father think I’m with someone else, and to a certain degree, I agree.

But I just cannot bring myself to tell my dad about my separation. He’s doing really bad and I can’t even imagine the disappointment and how hurt he will be if I told him my supposedly “happily ever after” is over. I’m a bit of a paranoid and a pessimist, so with how bad he’s doing during this treatment, I can’t stop thinking about him passing away soon, and with that, his “last big memory” of me (and mine of him) being of such a disappointment.