Hey! Welcome to the UF community Sadly I don't know much about the speech program, but Dauer is pretty close to Turlington, the Hub, and the Student Union, and is located towards the North East side of campus (www.campusmap.ufl.edu).
My first suggestion (and I'm echoing a previous poster) would be to go to padmapper.com and to a lesser extent, http://www.gainesville-rent.com/) and look at all the places that are near that side of town. Someone also mentioned http://www.apartmenthunters.com/Homepages/Gainesville.aspx, but to be honest I was much more productive looking at places myself. I actually live on the South East side even though my classes are near yours, and it's a very easy bike ride. Something to keep in mind is to find out if there is a bus line nearby that will take you to campus (for when the weather is lousy) and to grocery stores (assuming you don't have a car/bike).
Once you limit yourself to a certain rent range it will help you cross a lot of places off the list, then look at each place's website and cross off properties that look poorly maintained. I also looked at http://www.crimereports.com/ to make sure the neighborhoods I was looking at were safe. I narrowed it down to a few and took tours, asked questions, etc., and I also advise you to visit them at night/after hours - some places looked fine during the day but had loud parties and whatnot at night.
Most places you will find are pet friendly, just remember to negotiate everything - pet fees, rent, etc. If you have questions about specific properties, feel free to ask!