Have a look here:
http://www.houseinphuket.com/
They have a few short-time rentals available, although the selection is much, much better for long-term rentals.
Perhaps give Wellta a call with some of your other questions.
Mt TGF is spending her days looking around for a house to rent for us; she recognized the locations of several houses above and looked at them in person (I return on April 6th). She actually came close to putting a deposit down on one but now understands that I want to look at them myself before making any decisions (need to check out electrical wiring, plumbing, how quiet/clean the neighbors are, etc.). Now, I know a few more questions to ask -- although my past experiences with rentals in the States are the landlords don't care what time you come back home and who you happen to bring with you as long as you aren't causing big problems with your neighbors.
I'd be interested in hearing about any other local agents you might find, or if others think it's easier to deal with the owners yourself rather than going through the middleman.