I think that is a reasonable area. My impression of St Kilda was that it was quite big and urban. Very lively, full of cafes etc. Places like nearby Elwood, Brighton and Hampton as more laid back, familyish maybe even though they are just down the road.
To do with DCs? This is what I did during the day when DH was at work:
Aquatic Centre Albert Park (great toddler pools, slides etc)
The Zoo - very nice size and well laid out
Botanic Gardens
Eureka skydeck (88 floors up on Southbank kids loved it),
River trip (catch on Southbank in CBD).
Melbourne Aquarium.
Also go to Trampoline the ice cream store on South Bank (just along from Eureka) - no day was complete without a visit. Great foodcourt next door.
Things I meant to do:
The Arts Centre near Fed Square has an Art Play programme of kids events on different days of the week. They looked great.
Monkey Mania - Docklands soft play
Do get a car. It is easy to drive there and will open up the whole place for you. But parking in the CBD is extortionate. Best to get a tram in and pick up the free bus or tram that tours the city and down to docklands. Get by Fed Square.
Places to go at the weekend:
Luna Park (St Kilda only weekends) - though limited rides for a 3 year old
Healesville Animal Sanctuary - about an hour, fab place but wrap up
Phillip Island (cute little penguins, really worth it)
Puffing Billy at Belgrave
Crown Plaza - very lively at weekend evenings, light show, restaurants, shops etc etc
Ice skating at Docklands
Make sure you go to Tourist Info at Federation Square as it has loads of brochures which include 20% off this and 10% off that. There is one called Melbourne with Kids.