It is certainly possible in Gimp. A single pixel center line trace is not the easiest however:
Closely related to Inkscape in that autotrace is used. https://github.com/autotrace/autotrace/releases
That is called by a Gimp plugin, plugin-trace.py see: http://gimpchat.com/viewtopic.php?f=9&t=17485
Easier to set up in linux than Windows, packing in for the night but a first try (in linux) gives the attached. Will see about Windows tomorrow
Bottom line, you would be better off using Inkscape.
Closely related to Inkscape in that autotrace is used. https://github.com/autotrace/autotrace/releases
That is called by a Gimp plugin, plugin-trace.py see: http://gimpchat.com/viewtopic.php?f=9&t=17485
Easier to set up in linux than Windows, packing in for the night but a first try (in linux) gives the attached. Will see about Windows tomorrow

Bottom line, you would be better off using Inkscape.