I know it varies but I just want/need a rough estimate. I love that song and would really like to learn how to play it. I have a keyboard at home but it is never used unfortunately. I never had the opportunity to take lessons. 
I plan on taking lessons but I would like to master the song in the next month or so. Is that too ambitious?
Of course it depends on how talented you are, or turn out to be, and how well you want to play it. If you already know how to read music, and how to find the notes on the piano it might take a just few months of practice. I think one month to master it, having never played the piano before is a little ambitious. You might find a simplified version that you could play in that amount of time though. Good Luck.