IRLZ44NS mosfet + 3.3v gate
No you are not misinterpreting the data sheet and, if your load is 1 amp max you should be fine. Also, if you look at the next figure that shows the drain current versus gate voltage, 3.3 volts is not in the danger zone for creating a thermal runaway situation.

But, remember that these graphs are “typical” figures and not maximums or minimums. Having said that, on balance I think you’ll be ok.