Seriously, just get a gate driver or get a logic level MOSFET.
Q3 being an NPN type with 5V at the base will not allow the gate to even reach 5V
For some reason, you aren't taking these lessons seriously.
In my LED lamp i am just going to dim to a certain amount and below that i will just switch off. The IRLB8721PbFs will act reasonably well (Qtot = 8nC @5V) at the 20mA sourced by the Arduino for LED PWM ~300 ns switching.