Linking to a previous thread about creating a white garden which should provide some ideas. Discussion on white gardens

Be aware that the recommendations in the previous white thread were for someone in a cold zone, so be sure to check their suitability for your garden. I would guess that your zone is approximately like a zone 8 or 9 USDA. You will want to check my recommendations for the same reason.

White Clematis. There are quite a variety of bloom times, sizes, pruning regimens, and flower shape and size, so visit a good clematis nursery near you or see if there is a good mail order supplier in your area. I know Clematis can be grown in your climate. Ask specifically for ones with long stems so you can cut them. I don't bring flowers into the house so I won't make recommendations since I never notice stem length, and what may be available in Australia may not overlap much with availability here.

White narcissus - While you may not have enough chill time for most varieties, there are paperwhite narcissus which are grown as indoor bulbs around here that require no chill time, so check those out for earliest spring blooms.

White foxglove will send up new stems if you cut the flowering stems.

White peonies will be earlier than most cutting flowers. Old-fashioned Festiva Maxima has the bonus of a lovely scent and is very double, and there are many single and semidouble whites. They only bloom for a month or so in spring, but are covered with flowers for that time IME. I am not sure you can grow these, but from what I read, if they are planted only about 1/2" deep and given afternoon shade, they will work for you.

There are some iris that might work, though none bloom all season. In mid to late spring Siberian iris will bloom for several weeks if you choose a variety that has multiple buds per stem and repeat capacity. Some (not most) bearded iris will repeat, and I have a white one that does, blooming both in spring and in fall if the season is long enough.

Dahlias are probably perennial for you, and are long-blooming and available in white.

Annuals are programmed to bloom much of growing season, so look for taller annuals such as cosmos and zinnias which are available in white. (If you want cream, "white" marigolds will work, but there aren't any that are really white to my knowledge.) You could ask on the annuals forum about white flowers for cutting. Some of the things that behave as annuals for colder weather gardeners will actually be perennial for you.

You could also ask on the shrub forum for shrubs other than Hydrangeas (since you already asked on that forum) that are suitable for cutting in your zone.

Be aware of scents of the plants you are looking at since you will be bringing them into the house. For instance, I love Salvias, and many of them may well be appropriate for growing in your area, but in general the plant has a somewhat rank odor IMO and so I wouldn't use them for cut flowers.

How about white lilies? There are many varieties and some have that wonderful perfume!