JohnB.
Yes, you can replace the receptacle with a switch/receptacle. You can run a wire for the light out through holes in the top or bottom of the box. You can either connect the receptacle so it comes on only when the light comes on or connect it so it is powered all the time. If you buy the device it should come with enough information to connect it. One word of warning, make sure you turn the power off to the receptacle before opening up the box.

Ed
Probably not. It will depend on the wire size in the box It could be either 14 or 12 gauge. Since the switch is on a lighting circuit, it could well be 14. Your electrical code probably requires 12 gauge for plug circuits. Also apparently there is no ground wire. Again, your electrical code may require one on any new receptacle.