GIMP is a raster editing software.
Are you drawing with GIMP's vector drawing tools? If you do, then you could export an SVG file from GIMP and then open it in Illustrator and according to the GIMP manual you should be able to get paths out of GIMP.
If you're painting in GIMP and expecting to be able to be able to convert this into vector paths by pure magic, ou should definitely rethink your procedure.