Not aware of such a thing as a horizontal roller blind as you describe. Could you post some pictures and maybe someone will have a suggestion as an alternative?

Honestly, I think the best thing for you to do is to travel around your area and see if you can see what other neighbours have done. Or you could contact a local awning maker and see what solution they can come up with for you. No matter what's recommended on here, you need to decide on something that's easily obtained where you live. Hope you are having a good day. Fascinating to be talking to someone 'down under' :)

Bigreader is correct. Also, some people weave the hemmed canvas or late generation blind in and out of the pergola beams for the Summer then take down, clean and store for the Winter. Warning, canvas gets mouldy and a pressure cleaner is good. Shadecloth lets air through better.

Some councils have regulations about those, so check. Advise to pack it up when high winds expected. Otherwise good.

Grabbed one at random from Moreton City Council

Click on it

https://www.moretonbay.qld.gov.au/uploadedFiles/common/forms/building-plumbing/Building-approval-requirements-fact-sheet.pdf

We're getting a sail, and a lesson in how to take it down for the winter.