When I use the "save as" function of eog, it's more often to duplicate than to convert (example : I have the original photos of my hollidays in one folder, and I browse all and select some that I put into a special place to modify them or create a short diaporama with it).

So eog should "save as" the file (if no extension are written) as it is, so with the same extension than the original file.

Other information: