In my experience the lifestyle here is quite different from Australia. Everything opens late and closes late so a morning stroll to a park and a babychino is not common unless you are happy going to a chain cafe - starbucks, pacific coffee! Over summer it doesnt cool down at night much, so morning strolls in the park are hot and humid. We have an early riser so miss strolling to a coffee shop and taking a walk early in the morning, but we have found other interesting things to do instead
the beaches are good south side and often have small parks located on their shores which is a nice outdoor thing to do? Some of the apartment complexes (especially high rises) have playgrounds and indoor play centres located within them.
Otherwise, explorin the many parks in HK is great like HK park, Kowloon park (depends a lot on where you chose to live and proximity) or hopefully you will get a club membership as part of your relocation package which is where a lot of expat's with children gravitate to. There you have pools, playgrounds, activity centres, sport classes etc. and are a great way of getting to know people in your local area too with small children.
the Australian Association of HK may also be worth a look as they run playgroups and mothers groups around HK or the American womens Association.
Children generally start school/kinder here at 2 years 8/10 months so your lifestyle may change with that anyway? I know with our daughter the transition to kinder was big coming from Australia and she used to like resting at home after a morning at kinder.
Hope this helps a little?