Hello,
That size is fantastic

4x2x2 is avg rec for male adult.
Few questions for you....
1) You said you are converitng a "dresses" I'm guessing you mean dresser. So this is already built?
2) I protect the INSIDE of my wood using DRYLOK Latex based masonry waterproofer. You can get it mixed to any color you like at home depot. However it isn't the "prettiest" paint.
For the OUTSIDE, I use a nice weatherproof stain (rated for snowstorms) by Behr. HOWEVER, if you are using a premade dresser, depending on the outside, you can probably skip this step and be fine.
3) If you are planning to put the cage on the ground, so maximum height is 4FT, it would be "okay" but ideal is to raise her cage. I find personally, all my chams like to be as high as possible and come down to eat/etc and then go back high up.
4) Drylok + a drain on the bottom should make for a secure base that will last for a while. For extra security I would personally add a layer of thick painters plastic (its WAY cheaper than pond liner and if you use a ton and fold it up it works just as well).
Throw up a pic or PM me if you have any other questions
ONE WORD OF WARNING! Those cheaper IKEA units and similar are made of flimsy particleboard that will rot very quickly and are not very sturdy. They can work with proper waterproofing/etc. but just be careful of how much weight you trust them to hold (esp if you lift the entire unit up) and make SURE they aren't getting wet.