Is it a nice thing to do? No.
Is it a good thing to do? Depends who you're asking.
Make no mistake, you are screwing your boss over by quitting. However, as you yourself have said, the company you're with right now is offering no guarantees whatsoever. That job offer, on the other hand, is a certainty.
Here's some advice to consider when you're in one of these tricky situations:
Always keep your own interests in mind.
Your current employer sure as heck will do the same, and so will every other company you will ever work for - sometimes in your detriment. Don't feel that you should have loyalty to entities which will offer you none in return (aka 99% of all companies out there)
My personal opinion is this:
If you have been offered a full time position and you need it, then go for it.
The only thing I can't be certain is whether you should give 2 week's notice or not. I think it would make little difference as you've barely been there long enough to get anything done. Sticking around for another 2 weeks is probably simply going to be awkward for everyone involved.