Minimum MOSFET rating for MK3 heatbed
and welcome to the Stack Exchange 3D Printing site.

Let's look at the specs compared with the requirements.

How much power is used by the heated bed?  You have specified 120W (12V, 10A).  That information makes it easy!  On my homebrew printer it is higher, but that seems like a good high limit for a typical i3-style design.

So, the MOSFET you propose, assuming you completely turn it on, will dissipate 0.01 ohms * 10A^2, or 1 watt.  This will warm the part, and you probably should attach it to a heat sink, which could be as simple as the existing extrusions.  There is a much more complete answer to this exact question on the Electrical Engineering Stack Exchange site: Dissipating 1W on a TO-220 without heatsink?

I doubt the PID frequency is higher than 40 KHz.  Since the Vgs rating you referenced is specified with 10V on the gate, you can't drive that directly from an Arduino pin.  You need another driver transistor (NPN or FET) to drive the power FET gate.  The turn-on time for the power FET will be determined (in the simplest circuit) by the pull-up resistor to +12v connected to the output of the transistor and the gate of the FET.