MOSFET switch circuit design feedback
I would:


Ditch Q1/R7/R8/D2
Drive Q2 direct from the Arduino (maybe with a small resistor to limit inrush current, though not so large as to slow down the switching needlessly)
Use a pull-down to GND on the gate
Choose a MOSFET with a low enough \$R_{DSON}\$ at 3.3V
Make sure I chose a MOSFET that could happily dissipate enough heat for the current through it.








simulate this circuit &ndash; Schematic created using CircuitLab

(Depending on thresholds you may want to move the 10K pull-down resistor to the left of the gate resistor, but it generally doesn't really make any difference. It's only there to keep the FET turned off when the GPIO pin is floating at boot-up.)

Looking at the datasheet it looks like the MOSFET you have chosen may do the job. At 2.5V \$V_{GS}\$ the \$R_{DSON}\$ is (typically) 0.05Ω. With 0.6A through it you have 0.018W, which is much less than the 1.25W limit at 25°C.