Upgrade bathroom light and separate exhaust fan
Old school: probably not, unless the guy who wired that ceiling was generous with the wire. 

Cool new tech: Yes.  They make electronic switch controls which are designed to solve a different problem:  "I want a light AND fan, but my bathroom is wired for a light only."   This consists of a smart switch that goes in the site of the regular switch, and an electronic control module that sits in the fan housing.  

Now, I'm guessing your old fan has a vent - that is to say, a pipe leading from the top/back of the fan to the great outdoors. That will be a consideration.  Which is to say, if your fan/light combo is going where the fan was, that's not a worry.  But otherwise, you will need to be up in the attic reconfiguring that pipe... and while you're up there, you might as well rearrange the wiring to your preference also.