No entry stamp in Sydney?

Sod off.

Apart from Schengen countries, which of necessity use a common tracking system, the immigration authorities across other countries do not routinely share information about entries and exits. Why would they?

This may be rather under-estimating the degree to which today's immigration and border security | anti-terrorist authorities share information, and can access common databases. Some years ago I printed out my travel history just for fun, and it was remarkably detailed (if not quite complete).

How do you print out your travel history?

A month ago I rang up Centrelink to ask them something and I said I arrived back in Oz on xxx. They said it was the day before xxx, which was correct. It frightens you a bit, how much info the govt has on you..........

How do you print out your travel history?

I have no idea ... in the sense that I have quite forgotten. In fact I can't even recall whether it was via the US Government of the Australian. US perhaps.

Limited to the last five years I think.

If they want to check your bag, they would take hold of your passport.
They would not let you keep hold of it.
I just came back from NZ yesterday via MEL, and also they didn't want to have a look at my stuff.
Mind you, I have been asked aside before, and the will take your passport off you, if they want to do that.
If they just point you to an exit, than your lucky stars.
You can ask for an exit stamp, they will probably make a bit of a fuss, they would probably do it, but they might not.
All the groups you deal with, ie, banks etc, have access to a thing called VEVO, and if you want to work in Aust for 20 hours a week, or more during longer holidays, the people who pay you can check you via VEVO.
When you leave Aust, either for holidays back to India or NZ or anywhere, you don't fill in a OPC anymore, outgoing passenger card!
Call it progress, call it authorisation, call it magic, but its all electronic.
If you didn't use egate, and you went to a counter when you first entered Aust, your passport and data info is on computers. Each entry and departure is on computers.
You can as Westwood says, ask for a copy of it.

Raki me old chook mate, contact the ABF and ask.

My last blah, sorry OP, I was so shocked.
I came down the ramp at MEL int airport, from Auckland NZ, already used the Smartgate to print out that little receipt, and had filled in the IPC, and sheepishly asked which one they needed, thought I was going to get anal checked!
But nope, he just took the 2 pieces of paper from me and that was it.

It has been over 16 years since my daughter got her Australian passenger movements. She needed it for Centre link( though they weren't called it back then) to prove she had lived in Australia for 104 weeks. And of course, her record was missing the departure a week before she turned two. They had to accept the date I gave them as there was no proving otherwise. Maybe they are better at keeping movement records now.

All these kiwis pour into God's Best Little Country, and head straight to Centrelink to feed at our trough of human kindness ... how else can they acquire yet more tatts and recreational pharmaceuticals?

Don't worry about it, that's normal. And I am sure if you ask, they will stamp you on exit. My kids used to ask all around the world if they didn't get a stamp, and every security officer smiled and complied.