Anywhere from 2 - 5 feet.
Should be alright, I would put a 0.1uF capacitor from the arduino analogue input to ground just to get rid of any noise pickup.
will be able to determine if my dog is in his house?
Depends on how heavy the dog is.
How long do you think it will last?
No idea.
I did a project with home made pressure sensors:-
http://www.thebox.myzen.co.uk/Hardware/MIDI_Footsteps.html