To each their own....but ask yourself. Is this deer that important that you want it on you for the rest of our life?? I have several tattoos. Some I like, others I could care less about. Unless there was something very significant about the particular hunt with this deer, I would suggest waiting. My guess is you will one day shoot a bigger deer and you'll look back and say "why did I get this little deer tattooed on me"
Who knows, life happens and deer hunting may take a back seat o wife, kids, family, etc and no longer have the importance it does now.
Again, coming from someone with several tattoos, here is my advice. DO NOT get your tat done by the artist that drew that picture. The drawing does not look realistic, and is very amateurish. You will not be happy with it. An artists drawing should look almost exactly like the final product. The artist of that drawing may be good at certain things, but is to good at portraits and realistic tattoo. That's my honest opinion. I'd be proud of myself ifi drew that picture, but I'm not a tattoo artist....