Getting into a topic one is barely familiar with?
While your concern is perfectly valid (been there myself more than a few times), you should probably consider and accept that this is the way you are going to learn new things for most professional endeavors. This is how things work out of college; e.g. think about this: are you able to foresee what technologies and concepts are going to be required for your next project? And even if you could name them, could you set aside enough time for mastering them to be prepared for the next assignment?

As I see it, you already have a sound plan, I would stick to it. I would, however, recommend that you not get too engaged in just familiarizing yourself with the new environment. Sure, take some time to get some grip on it, but once you are got the basics, I suggest proceeding with your plan. One major asset of your assignment is going to be your new acquired skills, but that mastery will come in small portions along the whole road of the project. I find it unlikely (for students and professionals alike) to be able to learn a new paradigm in a reasonable time, without some means to guide the effort, e.g. class projects, so, instead of trying to get to the bottom immediately, get the basics and learn the rest along the way.

Other than that, as I said before, your plan is sound, just don't let the fear of the unknown overwhelm you into panic.