I did a Digikey search but I didn't see any filters that specified the minimum gate voltage to trigger the MOSFET. Any ideas?
What you're looking for is threshold voltage. Digikey list it as "Vgs(th) (Max) @ Id". Some value around 1V would probably be good.
Then you need to look at the datasheet to determine the saturation current you're going to see at your minimum supply voltage (less however much your gate drive differs from that). to see what load the device can switch. Also relevant is Rds(on) for this gate voltage. Both of these can be used to calculate the max load depending on the amount of heatsinking your device has (which you then de-rate for safety)
edit: OK I did this and picked the first N channel mosfet I found. it's a
NDS331NTR-ND, and it's
datasheet tells me that it has a RdsOn of 0.21 ohms at Vgs of 2.1V (it also gas a BVdss of only 20V) It's saturation current will be something over 3A (it's only rated for 1.3A continuous)
At 1A, the power dissipation would be 0.21W, and the junction to ambient thermal resistance is 250 degC/W, so the junction would rise about 52 degrees over ambient. That would be acceptable, but I'd label the device as being able to switch 12V at 500mA just to be sure.
You could go searching for other devices (that may be more easily available or have different specs) if you have a need for them. I don't recommend this part, as I said it was the first one on the list.