1 Hot Receptacle 2 Light Fixtures 1 Switch - Is it possible?
According to your diagram, yes it is possible.

You would connect it similar to your existing bathroom switch.  Run a #14/2 ROMEX (or other appropriate cable) to the light fixture.  The white wire would tie into the white wire on your diagram. The black would connect to one terminal of your switch, and you would connect the other terminal of the switch to the black wire in your diagram (the one on the bottom).  Bond the ground wire to the other grounds in the box or the ground screw.

Alternatively, you could power the new light from the existing switch.  With a 2 wire cable, connect the white to white.  Connect the black of the new wire to the red existing wire along with a pigtail (a 6" or so short wire).  Connect the pigtail to the top terminal of the switch.  This will allow one switch to turn both lights on at the same time.