The best way is to take hotel shuttle direct to your hotel, the shuttle bus costs HKD150 per person. The ticket office is located opposite to Exit B of Arrival Hall. If your baby is over than 3 years old, you should buy another ticket. If so, taxi is better. Taxi costs about HKD240 for around 70-80 minutes. Hong Kong MTR and Bus usually start running before 06:00 in the morning, some night bus would be earlier, you can take MTR and bus to airport, you time is enough.
Cheaper ways for your reference here. You can choose according to your situation, I mean how many lugguages and the baby.
Airport express to Kowloon, then free shuttle bus to the hotel. Cost: 90HKD, half the price for kid 3-11 years old.
Airport Bus Taxi: Take airport bus A21 to metropark Hotel Mongkok and then take a taxi to yours. It costs 33HKD less than 30HKD.