Low threshold N-channel MOSFET
It isn't hard to find a FET with a \$V_{GS(th)}\$ of 1&nbsp;V or less, but then a current in the microampere range may be a problem. \$V_{GS(th)}\$ is often specified at 10 or even 100 times higher current, so it may conduct at 100s of mV lower than that.

The solution may indeed be an NPN transistor. At near zero volt base voltage, you'll have a very low leakage current, but anything above 0.6&nbsp;V will give you an output current in the &micro;A range. A 100&nbsp;k&Omega; base resistor will do.