Just to say to OP that it's highly unlikely a decent doctor will fill a prescription for this as a "walk-in"...it's not a medical emergency (although I fully acknowledge that lack of sleep is absolutely, absolutely awful, and withdrawal from zolpidem is not pleasant at all).
How long is your trip? If you are going to run out with e.g. 7 days to go, you could just ask your primary care physician for 7 days' extra prescription. The main concern is that it is quite common for these tablets to be sold-on illegally. If that still doesn't work, you could book an appointment with another physician in the same practice and explain your plight.
If that _still_ doesn't work: I would suggest that you start taking a slightly smaller dose as of now of your zolpidem. Most patients (making certain assumptions here, but really the vast majority) will be absolutely fine with a smaller dose as long as there is no abrupt withdrawal.
Good luck!
tb