hey orinoco. its not quite that simple (i have a property renovation business btw). even if it is a stud partition wall, the stud may be load bearing. its ALWAYS best to get someone who knows what they are doing to check this.
after that, you will need to pull off the plasterboard (you can definitely to remove only the upper portion, though what is possible will depend on the stud behind, and then the timber.
you will need a plasterer to make good, and possibly some carpentry too if you "halve" the wall.
finally, you need to be careful of any electrics therein. even if you have a go at the rest (definitely, post struc engineer to test load bearing aspect, something a competent diy-er could do) you must not do any electrics yourself. it is serious and dangerous stuff.
oh, and i forgot to add, differences in ceiling/floor heights would make it trickier.