How to use MOSFET as a switch to drive LEDs
The MOSFET gate current will be zero, unless you have a broken FET.

Choose a logic level drive FET. These are specified to be well on with 5v or less on the gate. Most 'normal level' FETs will be sort of on by 5v, but their resistance is only specified at 10v gate drive.

At 150mA, almost any FET will do, including the SOT23 sizes. But check in the data sheet for the drain current just to make sure.