So in my opinion, it would be ok to protect beyond what the electrical
code requires and place the light on a GFCI as well, however I like to
wire the lighting on separate circuits so you have lighting if an
outlet breaker/GFCI trips. Thus I think it would be better to place
the light on a separate GFCI or a separate GFCI breaker/circuit if you
must. And of course I would check with your electrical inspector first
to see if there is any reason he would not allow this.

The shower hi-hat is on a seperate circuit than the vanity light and 2
other hi-hats in the bathroom.So even if the GFI did trip, there would
still be light in the bathroom.