...yet another moving to Sydney post

My family (wife and 1 year old daughter) and myself should be moving to Sydney in about a months time. I received a job offer to work for an accounting firm. My future office is located on Market Street. In terms of salary I will be making approx. AUD 5.300 a month net.

Now that you have a bit of info, a few questions:

1. I have researched rental property online left and right and have decided to spend about 1.600 to 2.000 a month on rent - is that reasonable? In terms of locations we like Pyrmont, North Sydney, Sydney itself (close to offices) and Darlinghurst. Pyrmont seems quite close to Market St. but how long is the commute from North Sydney, Darlinghurst or Mosman by public transportation?

2. Is Darlinghurst safe? I've heard it's not the "nicest" area to live in especially with a small child? The thing is - i like the new apartment buildings there (i.e. Monument).

3. In terms of living expenses, would for example AUD 2.000 cover our cost of food, utilities, etc. (my wife will probably not work in the initial period and will take care of our daughter).

4. How necessary is it to have a vehicle? Is the public transportation network OK? We're from Europe and our PUblic trans is very well developed so how does down under compare????

Will probably have a ton more questions but those are it for now. Sorry for bombarding with all these but we're trying to find out as much as possible and have a million questions in our heads!!!!

Thx in advance....