Great points. I believe it was ThinkHard who said you can fly round trip to Turkey this time of year for $393.00, and someone else (maybe the same person) said the Hostel wouldn't have cost more than $100-$200 total. In addition, there's spending money, food and the trip to Amsterdam and Munich to factor in. I think compared to some vacations, this one falls on the less expensive side of average, but for a family who is already on a tight budget, she'd have to save probably at least a thousand bucks in two months' time.
I also know she was a college student. I know it's not totally kosher, but I've known students who receive financial aid checks above and beyond the total cost of tuition. They put those checks to use on other things- vacations, other financial obligations, that sort of thing. Maybe she paid for part of the trip that way?
As for getting the time off from work, that would be another challenge. I work in Human Resources and can tell you that generally speaking, employees that are hourly and part-time are not give standard vacation time. That doesn't mean they can't take a day off- it just means that any time taken off work would be taken without pay. Being a new employee, I'm surprised she was able to convince her boss to give her the time off, but sometimes employees will negotiate that sort of thing prior to their start date. In other words, they'll take the job offer, but will say, "I have a trip planned to Turkey in January. I'll be gone three weeks, is that ok?"
OR- maybe she got this job for this specific reason, and was putting her entire paycheck aside for the trip. If she did it that way, she could probably save up enough money within 2-3 months, I'd imagine.