Dragon Age Awakening on 12GB PS3

I have a 12GB PS3, and I bought the Dragon Age package that includes "all downloadable content", presumably including awakening. However I'm getting the impression the content isn't actually on the disc, I just bought the right to download it. I haven't been able to install Awakening (obviously, it's bigger than the PS3 drive) and I think I'd have the same problem with some of the other content as well. Is there a way around this, so that I can play the content from the disc? (And I mean without having to upgrade the hard drive on my console).