Syringe pumps deliver their contents VERY slowly (in the range 10ml per hour; probably less for rats?) and hopefully very regularly. Picture one of those 4 RPM timing motors driving a precision ball screw, pushing the plunger. Just the thing for keeping your wife painless during baby delivery 
Servos don't have enough resolution.
A geared stepper motor driving some sort of screw arrangement is probably a good start. In fact, you might start with a computer's CD drive; they usually have a stepper driving a ball screw to move the heads (over 30mm or so of travel distance.) Insert a bunch of gearing in between the stepper and the screw, afix some sort of lever to the head to push the plunger, and you'd be pretty close. You'd even have a sturdy platform to mount things on.
Hmm. They seem to also get used in rep-rap like machines (extruding polymers for 3d-printing.) And they show up on eBay quite a lot. (Some broken. Although adding arduino-based electronics to existing mechanics might be a viable strategy.)
http://blog.reprap.org/2005_03_01_archive.html
I don't know how publishable research is when it's made using "questionable" equipment. It may divide into two catagories: "Your homemade XXX is very clever!" and "Your use of homemade YYY completely invalidates everything you've done!" (There was a recent study done of "software quality" in lab equipment of the sort made by people who studied, you know, biology or chemistry or one of those other real sciences rather than spending a decade or so in the software industry figuring out the many reasons that SW breaks all the time. It wasn't flattering... (sorta like: "people who studied computers and spent their careers writing SW still produce crap. What did you expect from people who took two CS classes in college and went into lab research?" Ouch.)