The tune is mentioned here as being composed by Eileen O'Brien.

I'm wondering if there are OTHER Jennifer's Waltz, as there was another site which claimed someone named Jeromy wrote it for his wife.

It's apparently popular enough to be in at Dobro Tune book from Mel Bay. (Or at least a tune with this title). Hey, if it's popular enough for Dobro, perhaps it's something the Bluegrass people might know?