First of all, the first thing you should do is reflect on this:
Why I didn't try to negotiate the duration is a whole another story, but I had good reasons.
It sounds like you've known long before you even started the application process that you would be going on a vacation. There is really no excuse for you to hide that information from your employer.
But as you said, what's done is done. So what now?
First of all, what you're describing sounds awfully similar to the PEY program at my school, so I've been through the experience.
Generally in this program you can choose to do 12~16 months. Rarely do companies require you to do 16 months.
Even if they did, an internship is still an employment, and according to any reasonable employment contract, you have the right to quit your job. There may be rules such as a two week notice, but it's clear that it's not "illegal" or "BREAKing the contract" to quit the job a month early. People sign one year work contracts but that doesn't stop you from quitting the job if you're unhappy.
So now that we've established that you're ok and your life will not be ruined, the question is: how can you do this and not look bad?
The answer to that is similar to the other answers. Bring it up ASAP. PEY end dates are usually flexible so it's very likely that they'll just say "OK" and you're set. No reason should be needed to want to take some time off after 16 + 8 straight months of work and school.
Whether or not you get hired back as a full-time really doesn't hinge on this either. That is decided mostly on whether or not you were a good performer, so do a good job. :]
To summarize, try to bring it up soon after you start working there, before it becomes "too awkward to bring up since it's been so long". The worst that can happen is that you will need to quit your internship before the time is up.
Lastly, I think that it would be ok to say that the vacation was planned by family after you signed, if they ask, and hope they don't see this question ;). Again, next time, be more up-front about this kind of stuff!