Elsa,
Please don't take offence, Cobra owners are usually very protective of their cars. There are several good reasons for this. Most of them have been lovingly hand built over many years costing the owner a lot of time and money. They don't easily risk letting another drive their pride and joy especially a stranger.
The other reason and I think the more important one is these cars are dangerous in inexperienced hands. Most have more power than they know what to do with in a light weight car with a short wheel base. Get it wrong driving one and it will bite you.
We often get requests for joyrides for birthdays and for weddings through the Victorian Cobra Car Club and very often the requester's dream is fulfilled. However I think you will be hard pressed to find someone who will hand over the keys.
Try getting in touch with the WA Cobra Car Club. One of their members might be able to help you. Here's a link to their site:
http://www.cobracarclubwa.com/
Good luck