Flight
From Sydney Airport, Newcastle is approx. 2.5 hours away by car. Redhead itself is about 15 mins closer to Sydney. Trains are available to Newcastle from the train station at the airport, which will likely take closer to 3-4 hours.
Flight
Newcastle also has an airport, which may be available for domestic flights from Sydney if desired. Please note the the Newcastle Airport is 30-40 minutes away from the Newcastle CBD and 45-60 minutes away from Redhead.
Train
Trains leave frequently from the train station at Sydney Airport. The simplest route would likely be to catch the T8 from the airport, and get off at Central Station in Sydney. From Central you would navigate to the platform for the Central Coast and Newcastle Line. This line will take you all the way to Newcastle, where you can depart at Broadmeadow Station or in the CBD at the Newcastle Interchange Station (or others in Newcastle depending on where you are wanting to go). From Newcastle, your best bet is taxi or Uber to Redhead.
Travel Note
There are 14 car rental depots at Sydney Airport and many different companies to consider. Car rental companies include: Alamo, Alpha Car Hire, Avis, Bargain Car Rentals, Budget, Dollar, East Coast, Enterprise, Europcar, Everything Fleet, Hertz, No Birds, Sixt and Thrifty. I have personally used Budget, Avis, and Hertz before and have never had any issues.