Find as many prices for similar Corollas so you have a value in mind that you can demonstrate to them.
If you want to have it repaired, bargain for the right to the car, as many companies pay it out then take posession and auction the wreck.
I'd expect it takes a tiny accident to write these cars off, labour at panelshops is so expensive that minor accidents are writing off 10yr old cars now. I'm amazed as what I see at Great Western Wreckers.
Best-case I expect will be to get a thousand bucks from the insurance company and retain ownership of the car. Then you need a mate who is a panelbeater to help you strip and repair it. A chassis machine can pull a chassis straight, or a donor car can be cut and the rear-end welded into place.
Look up regulations for statutory writeoffs, you don't want the car declared that or it can't be repaired for the road again.
Good luck-