What is the best way to get from Phuket to Ao Nang? Ferry, Bus or private car? What is the estimated time and cost? We are traveling in December - do we need to book this now or can we do it when we reach Phuket?

You will be able to hire a car from a local travel agency that will take you from Phuket to Krabi. Make sure you don't use one affiliated with your hotel, but a more local one. This will give you the best price.

About 3 - 4 hours depending on transport, car can be much less than 3 hours. Hire a car, or take a minibus or local bus from Phuket's southern bus terminal. Buses leave from Phuket daily. Information regarding bus timetables, taxi or mini-van shuttle services can be obtained at hotels, travel agents or Phuket Airport.

If you are going by road,take Route 402 to Route 4 and pass Tambon Koto Kloy of Takua Tung District in Phang Nga; Tap Puhd District, Phang Nga; and drive through the Ao Luk District of Krabi. A number of buses run this route from Phuket daily, taking around 3-4 hours, or alternatively, taxi's or air conditioned mini-vans can easily be arranged and are much quicker. Information regarding bus timetables, taxi or min-van shuttle services can easily be obtained at the airport in Phuket, hotels, or travel agents.

Please scroll down on the below website. It looks like there is a direct ferry from phuket to ao nang which takes ~2hrs. Is this information correct

http://www.railay.com/railay/intro/getting_there.shtml

Yes, that information is correct. This ferry runs from November to April only, so for your December trip it is an option. I believe there is only one ferry per day which departs at 08.30.
Destination Air who are also listed on your link are not currently operational.