My husband and i and my first born are all australian citizens with aussie passports. My second child was born in HK but we are yet to organise his passport
It hasn't stopped us travelling there however. Our travel agent simply organised a visa. It was free of charge and took a day. It ended up being a photocopied bit of paper that we tucked into my husband's passport. I'd do this. You'll have just had a baby. Concentrate on that for the first few months, have your holiday, then come back and arrange the passport.