You'll be fine driving on the correct
side of the road- the first 10 minutes will be full of impatient Sydney motorists honking at you, then you'll get the hang of it. That's how it was with my non-English speaking friend from Paris who hired a car for the same trip.
Much of the drive up to Katoomba is uninteresting, but once you hit the foot of the mountains it's lovely.
Can you be flexible with the day you visit? As Annalise pointed out it could be a waste if you go on a bad day. When it drizzles it's truly miserable up there.
Stop off for a drink at the Carrington cocktail bar - in the main house, not one of the bars on the street. It's a highlight that a lot of people overlook, a real taste of early 20th century Katoomba when the town was at its best.