I would go look at another 338rets and take measurements and cut by that.
That is really odd that there is no vent. I don't recall having ever seen a large bedroom like that with out a vent.
You may have to trim the cut with 2x2 on the inside after cutting. You can buy a vent cover from Walmart cheap to use as a pattern and then use the metal or plastic surround that drops in the hole.
When installing the ac don't over tighten the rods that sucks it down. If you see the metal flange start to flex your good.
I place a ext ladder beside the unit with a old rug placed against side and across top to cutout. I tie a rope to the unit , cover removed, then slide up the ladder until I can grasp by hand. A friend helping would help.
Best price is off eBay, get the unit with the inside part included for the best price. You can't use ducted, get the regular non ducted.
Come on down, I'll help you. Be done in an hour.
2015 338RETS Eagle Premier gloss sides., king.
2012 Ram 3500, crew cab 4x4 duelly Deleted
16k miles, 530HP, 1000 +torque.