Doomed Or possible? dating a younger woman?

[Stevepro68]

I am a 50 year old male. I don't specifically go looking for younger women. The physical attraction is obvious, but talking to young women fails to keep me interested. I am divorced and became friends with a younger woman. I am a realist, she is so beautiful I never really considered her obtainable. She is a woman that gets a lot of attention, and I'm an old dad bod guy. She is 33 single no kids. Beautiful blonde fit with an engaging European accent. We would talk for hours, and we started hanging out without our coworkers occasionally.
She is very smart with money, educated, we both are set financially.
She has a fascination with things from my generation other than me. Old movies, music, literature etc.
We seem to click on so many levels, for some reason I can't fathom she finds me very attractive. I didn't initiate our relationship we were sitting at a bar, our coworker went to the bathroom, and she kissed me. Sex is amazing as you would expect. She is not shy about demanding physical attention. Sometimes I am just sitting on the couch reading, and she walks in wearing lingerie. I DO NOT need that level of enticement to be turned on by her.
She likes to tease me about my liberal leanings politically, we trade books and discuss them for hours.
Admittedly, I look young for my age, most women guess 40. Full head of hair almost zero gray. On another level it's weird to think that her father and I were both in elementary school at the same time.
When I am with her it's just awesome. When I am away from her I just think things are too good, and the other shoe is going to drop.
Never dated someone this much younger than me. It's been a year, so now I think it's real. After my divorce I am paralyzed by the thought of combining lives with someone. Yet, she is frequently hinting, that she wants to go the next level of our relationship. Move in together.
I am sure there are young people on here that have lived something similar. Do you think it will work out long term?

Updates:

[McMillanD]

Personally, I never understood the appeal of dating someone so far out of my age range. I couldn't imagine having that much in common.
However, my best friend is dating a man who is 25 years her senior. She is young and beautiful and I did not understand at all why she would choose him over the other guys her age. Yet they have been going strong and living together for going on 2 years now.
So I asked her why.
She told me that she didn't see the difference. What she saw was a good man who was exactly what she was looking for and age just wasn't a factor. Sometimes we meet the one early on and sometimes (at least for one) they have to wait a long time. But regardless of WHEN it comes around, you need to grab it by the horns and hold on for as long as you can.
Which made a lot of sense to me.
What I know is, as long as you are both happy right now, who cares if it will last forever? I wouldn't go throwing it away early if it is amazing now. No one knows how much time they have and living with fear of the end only expedites the process. Love her now, and love her good, if it ends it ends but you can say that you gave it your all, and it was good while it lasted.