Those FSR's are pretty expensive.
You might want to spend some time playing with capacitive sensing, but it doesn't have to be this kind:
http://arduino.cc/playground/Main/CapSense
The human and the foil make a capacitor there. Change the distance between them and the capacitance between them changes. But you can take two pieces of sheet steel and do the same. Put a piece of insulating springy foam between and you have a pressure sensor that can also work as a proximity sensor.
Of course you could go about 1000x simpler and just put the dog bed on springs. When the dog lies down on it the springs compress and two contacts meet... viola, an on switch. Just keep the volts and current low, don't use aluminum, and you won't be cleaning corrosion often at all. Throw in a thermostat and a logic gate or two and you can have it warm the bed when it's cold, run the fan when it's hot or do nothing when it's nice out all without needing a processor of any kind.
Aluminum in contact with other metals and current flow in the presence of oxygen results in corroded aluminum. Conductive paint, or sheet steel, better for long-term. You can paint steel to seal it with ordinary oil-based paint.