According to the statement on the LEMB here
http://www.luftwaffe-experten.org/fo...howtopic=15609 , post 34, given by Mr. Martin Handig, the co-author of the book Die Deutsche Luftwaffe in Österreich that can be found here
http://www.oefh.at/sonderdrucke.html , the creature was indeed the windhund or greyhound.
"... Reading the JG7 Verbandszeichen: it is not a "wild weasel" nor a "running fox", as you can read in uncountable publications. I know for sure this sign refers to Rudolf Sinner (Austrian), who had a Greyhound dog breed collection and he therefore proposed the Greyhound ! This is first hand history by Sinner himself, who shared this true story with a good but unfortunately recently late friend of mine and of the late Rudi Sinner..."
Regards,
Sinisa/Sidney