On separate tickets, BA will only tag your bags to Sydney.

So yes, you will need to fill out a landing card, go through immigration (if you can use the e-gates then this is painless and quick), collect your bags, go through customs and then take the elevators upstairs to LATAM check-in. There is no airside option if you need to collect bags.

You should have plenty of time before the LATAM flight so unless BA15 is terribly delayed, the collection of bags and check in is a minor hassle. Just be aware of the customs rules on entering Australia and declare anything you think might need to be declared - but since you are travelling on to NZ who have similar bio-security this shouldn't be a problem. (If you do need to declare anything you have to use the red channel and it can take anywhere from 10 mins to an hour, depending on what other flights have landed - but still plenty of time before the LATAM flights.)

Or is there an issue with the length of visa you have?