The Arduino store sells the 12V 12W (1A) model and the schematic shows that output goes to Vin. You can get 12V 1A from the Vin pin and regulate it yourself or draw up to 1A from the 5V line (5W) and hope the regulator can dissipate the heat (the other 7W turns into heat).
POE module datasheet:http://www.semiconductorstore.com/pages/asp/DownloadDirect.asp?sid=1353084202849
You can also get the POE module in a 5V 9W (1.8A) model. You'd have to route the output to the 5V line since the regulator on the Vin line needs more than 5V in to get 5V out. Then you'd have 1.8A of 5V to play with... as long as the traces on the Arduino don't fry.