These were comments, but I turned it into an answer because it really is an answer to the question. I'll edit this into a better format when I get back from work tonight, if I have some time.
I wouldn't drive this FET with 3.3 V. It's only rated for drive voltages of 4.5 V and 10 V, and if you look at figure 12 of the datasheet, the on resistance at 3.3 V is many times greater than either of those. You might have a hard time finding FETs with really low on resistance at 3.3 V; I would at least drive it through a cheap gate driver (or even just a TTL inverter) powered by 5 V or more.
Always be sure to check that your FET has some sort of usable on resistance at the voltage you intend to drive the gate to! The IRL series from IR/Infineon are "logic-level" FETs, intended to be driven by logic signals; usually 5 V but some have ratings for lower voltages. The IRL6342, for instance, lists typical on resistance of 15 mΩ at 2.5 V drive, so perhaps that's worth looking into.
Since I don't know what's available to you, I would suggest looking into just using a TTL inverter. You can get those quite cheaply--some in tiny packages like SOT-23-5--from various manufacturers. TTL (or CMOS with TTL-level inputs, like the 74HCT series) is handy for this sort of thing, because regardless of the voltage powering the logic, the input high level is anything more than about a volt, so you can use it to shift voltage levels quite cheaply. Makes a decent gate driver if you don't need anything with amps of drive strength.