You need a contents policy that covers you for accidental loss and accidental damage, anywhere in Australia/NZ. You need to have enough sum insured that you will be able to replace all your contents, including all your handbags, at today's prices- brand new. It doesn't matter how old your contents are, you want to be able to replace them with brand new items. You also need to be sure that your handbags are covered as contents items, not "valuables" or "special items" or similar. You need to make sure that the item limits for your handbags are high enough that you don't need to specify the bags individually.
I'm really concerned that you don't currently have insurance, because you live in a high security apartment. This may be ok in terms of burglary, but what about fire? r earthquake? how would you replace all your clothes, bags, shoes, furniture etc etc if a fire burnt your home down?
I have several LV's, Chanels, Hermes including a Birkin that would cost $12000 to replace, and my contents insurance covers them all, without having to specify any of the bags. If you want more information, pm me. (hint: I work for an Aussie insurance company).