I once was doing a liquor promotion a few years ago and a store manager told me the story of why there is a deer on the logo...not sure how true it is but it does seem interesting. The man who created Jag, Wilhelm Mast, loved to hunt deer and was known for his many "prizes" on his walls. One day he went hunting and aimed his rifle at a deer when suddenly, the deer glowed and a cross was showing in between its antlers. Mast put the gun down and from that day forward decided he wanted to create a digestif.
The closest font to Jag is called German Gothic. I feel like the s in the label looks more like an f, the Uppercase J looks like an F and the r's look more like c's, making it close to the font Wilhelm K...sch LT Std. There are too many added serifs to the letters that it looks somewhat confusing as to what it says (at first glance). Also notice how the J descends more than the g and the g descends more than the s. I personally think a better font for the bottle-- keeping up with its old-fashioned tradition-- would be Wittenber...tur MT Std or Goudt Text MT Std because they are more readable.
Can you see the "confusion" of some of the letters in the logo? Do you like the font or would you change it?
Sources:
http://en.wikipedia.org/wiki/J%C3%A4germeister
http://www.abstractfonts.com/font/6977