The power dissipation of them is 1.25w at room temp and I'm going to be running 12v through them - plus driving the gate at 5V. I'm a bit lost with the formula?
If you are using them for static switching - either on or off, no fast pwm or the like, then 4.9A right from the first page should be your value, dissipating 0.8W and rising 96°C above the ambient temperature, i.e. really hot but managable.
+/- 12V is the absolute maximum, not required Vgs. Not only do they state the max current at 1.8-4.5V Vgs, but they also state Vgs threshold as 1.2V max.
If you are using them for static switching - either on or off, no fast pwm or the like, then 4.9A right from the first page should be your value, dissipating 0.8W and rising 96°C above the ambient temperature, i.e. really hot but managable.
N.b. the ratings are for the FET "Surface Mounted on FR4 Board, t ≤ 5 sec."
If you are PWMing the FET it will dissipate more heat than if switched only occasionally. You should reckon on handling less than 4.9A (the specified absolute maximum) for reliability.
If your switching is > 25Khz, you should use a dedicated MOSFET driver chip to prevent FET overheating due to linear mode transitioning. Otherwise I'd still advise a bipolar transistor like a 2n3904/6 to drive it. Direct from a 20mA max logic gate or uC pin is ok if you're under 10Khz or so.