You can claim your whole internet costs, doesn't matter what it's used for. You should be able to get a statement from Optus so you can claim the $ that you spent with them as well. There's a list of the things you can claim on the ATO website, plus FAQ which are worthwhile checking out. If you do it over the phone, you don't need to send the receipts in unless they request them later on, so you've got a bit of time to collect those you don't have.

Did you keep the receipts from the school supplies you bought for this year (pencils, books, etc.)? That's claimable as well.

For my 2 school age kids, I claimed the whole $750 for one child on a new computer, then the other child had the remainder of the computer cost for hers, plus several months worth of internet costs to take it up to the $750 for her.