I haven't had the Peeper Ale, but the people over at Beer Advocate are apparently pretty big fans! It sounds like they are putting some malted wheat into their pale ale recipe (which would explain the fluffy white head and slight haze people report) and doing a good mixture of piney and citrusy hops throughout. I would think you could experiment with things like lemongrass, orange peel, coriander, and clove to try and get some of the flavors and aromas that are coming out of it.
Of course, the easiest way to bypass all of the experimenation is to just call them and ask! Most places won't mind telling you some or all of the ingredients they use, they just won't give you the exact recipe.