Welcome to Melbourne, LostinAusNation.
I think "good" is the correct response until you know someone well enough to say exactly how you really feel.:o
I know the feeling of being more settled after the initial looking about, and glad you feel better.
There are some MNers here but the PomsinOz forum is very good for getting to know people in suburbs near you, e.g. Point Cook meet-ups or Mornington.
I don't know what Australians eat but we have oysters, prawns, crayfish and potato salad for Christmas dinner, and an Aussie recipe Christmas pud to follow. We did lunch on the beach one year, and yes, no-one else was there. We set up a gazebo, spread rugs and had great time. We live in a seaside suburb, so this was easy to do. This year it will be the above food, but either on the deck at the back or front of the house, depending on the weather, though that promises to be good.
I understand Australians have dinner at home, then do yard cricket, that is run by the men, who are obliged to let the children win.
I'm guessing they might do the beach in the afternoon, but as Port Philip beaches aren't surf, they don't attract the tourists in the same way as Bondi. Which is good, as Bondi is not very pleasant IMHO. All this means, it's not touristy, and the people you'll see will be, on the whole, Melburnians paddling in the shallows, taking the sun, cooling their toes.
Depending on where you are, there a number of beaches good for small children, e.g. Rickett's Point, Safety Beach, or anywhere where a surf life saving club exists.
There are lots of places you can book a Christmas lunch, so again I'd look at ones by the sea for that post-prandial stroll.
One thing I can vouch for as being thoroughly Australian is the mowing and edging of the nature strip in time for Christmas. They're out in droves; I can hear one now.
Have the happiest of Christmases. 