Should I quit my job?

I'm a first year at university, and got a job that I started at the beginning of October. When I first applied I told the manager that I was a university student and would like to return home for the Christmas holidays, and she said there was a possibility of transferring to the store in my home town. However, I just found out that wouldn't be a possibility because of the probation period not ending until after the Christmas break. I don't have enough holiday to cover the entire Christmas holidays and a lot of Christmas has already been fully booked off anyway before I started working there, and despite the fact I only would've worked there for about two months, I'm wondering if the best course of action would be to quit and get another job. I do want to go home for Christmas, and since the break is several weeks, it means I'd have to travel back to the city for work, which would roughly be £14 to get there and come back, and thats not including the fact a lot of my shifts tend to be spread out and there's a good chance my manager will say no to grouping my shifts together. Not to mention, from my halls it's an hours walk or I have to take two buses, meaning it's a lot of travel during Christmas, and since I don't get paid a lot it could add up quickly. Is returning to their university city something people often do? I'm very worried about the idea of quitting since I've only worked there not even a month so far, and I'm worried about getting another job in January when I was very lucky to get this one, but from my perspective it doesn't look the most feasible. Is it actually a good idea to quit, or should I be sticking it out?