Can I refuse to go to a surprise vacation paid for by my girlfriend?
Free vacation is nice. Why wouldn't you go?
I don't trust her. Sometimes I think she's secretly unhappy despite her cheerful attitude.
I can understand your anxieties, but this shouldn't hold you back. I think you need to talk to her about things that may be bothering her so you can fully enjoy your break with her.
I have so much work at work that I can't afford time off, I don't want her to resent me for not going.
That is a good, legitimate reason. It's also a bummer that you can't mention the vacation because it's a surprise. I think you need to act fast and let her know how busy you are, that you absolutely do not have free time and it would be impossible to take vacation time off.