Does your university have any statistical consulting services? If you background in statistics in general is limited and you only have limited time, then learning R will not be enough, you also need someone who does understand the statistics enough to tell you what you might be missing. You may be able to do most of the work yourself, but you really need an expert who can look at your project (as early on as possible) and tell you if you are missing something important, or can confirm what you have done is sufficient for your question.
I have several non-statisticians that I work with who are savey enough to do a t-test or simple regression on their data, but they still like to run their projects past me. Most of the time what they did is fine, but they are happy to hear me confirm it. Sometimes there is something that is beyond their knowledge (how to deal with censoring, non-simple samples, adaptive designs, ...) and things are much better if I help them do the correct thing rather than let them do something that is simple but wrong for the situation.
That said, in the long run learing R will be useful for many uses, not just a single masters project.