Burning a Uno bootloader into a Nano
Assuming they're based on the more recent Arduino Nano 3.x series or later, the microcontroller in your Nanos is probably an ATmega328 running at 16 MHz. That's the same as the Uno, so there should be no major problems hopefully.

It might be worth checking that you've got the latest version of the Arduino IDE though. I seem to remember there was a problem in some older bootloaders which prevented the watchdog from working properly.