I tend to agree with you about Jennifer but was thrown when I realised that Jennilee would fit just as well!
My mother-in-law is a Jennifer so it will probably prove the safest way for me to go!
The sources I could find suggested that Jennifer was of Welsh origin but then again as there is the Gaelic/Celtic language connection and the name is supposed to be a corruption of Guinevere, so who knows?
I would agree with Sarumite...In Chambers Jennifer is given as the orig.Cornish form of Guinevere, which in turn is given as.. (OFr, from Welsh) 'fair' and 'soft'.