Ditto many above suggesting alternatives. The sentiment is awesome, but that's a lot of money to spend without discussion and during a situation that for her is pretty unknown. For example, you say she should be free in the evenings, but since the trip is school-related, that may not actually be true: she may have studying or research or other similar work she needs to do.
A large part of the experience for her will also be networking/bonding with the other people involved, which could help her both personally and professionally, and under what I'd guess will be intense/accelerated circumstances. If I were her, I'd feel like I was being put on the spot (however good the intentions) to have to mix and balance my work/education with my personal life without warning, which would make neither particularly enjoyable.
I'd say "Go for it" if she were away for a year, but over one month isn't very long, and honestly, as a woman, I wouldn't appreciate suddenly being put in a situation where my colleagues (whether correctly or not) might see me as less professional somehow. It's stupid, but women already have a tough enough time in STEM fields (see Tim Hunt and #distractinglysexy), so I wouldn't want to do anything that could distract her or impair her situation.
I say talk to her, make the surprise the whole idea in general, and let her decide when is the best time for you to travel for it.
ETA: And happy anniversary!