David gave good advice abot letting the wood season a before painting. PT, unless it is kiln dried, is too wet.
Do prime it, with an oil-based primer. Then if you have to paint, paint with two top coats of a good quality latex paint.
Can you get away with a solid-stain topcoat instead of painting? PT is usually SYP, which is fairly unstable. As the wood moves, the paint may not be able to keep up and cracking/peeling paint will be the result. Especially if the doors are not undercover or have high exposure to the sun.