I can see two different scenarios here when you're saying that "she wont let me go":
is it in the tone of
1) "HELL NO! YOU'RE NOT STEPPING OUT OF THIS COUNTRY WITHOUT ME!"
or is it
2) "I really do not want you go on this vacation without me. I know we've planned to go on the trip, but I would really like to you to go with me on this trip...."
if it is the first one or closer towards the first one, then i definitely say that you should go. however, if its the second one or closer to the second one, then i think you should consider rescheduling the trip. Like you said earlier, finding a job isnt easy. I am pretty sure if she had a choice then she would have waited until after the trip to start. You can't fault the girl for not wanting to bum off of you all the time.
A trip to Japan isnt exactly a once in a lifetime kind of thing. If it's the vacation days that is stopping you, then you can always get more. The money thing might be an issue, but with your gf having a job, then it will be easier to be able to pick up and go in the future. Hell, it will even be more fun with her bringing in some cash. The difficulties that you spoke about in getting a passport isnt an issue, since you already got it now.