Just identifying the vehicle rego isn't enough to identify the at fault party
If you are insured and can provide the at fault drivers details, you shouldn't have any issues making a claim through your comprehensive policy*. But it's critically importance to identify the at fault driver, the vehicle, the location and the date and time of the crash...
Usually, in these cases, you wont have to pay excess though some insurance companies may want you to pay excess up front. When you are asked to pay an excess when not at fault, this excess is refunded when costs are recovered from the at fault party. But even in these cases where the costs aren't recovered, because the insurance company decides it's commercially not worth chasing some poor smuck through the courts, there is still hope. As the insurance company is not looking after your interests under the policy, I've successfully argued they aren't fullfuilling their implied promise to protect me in such cases. Since it's a commercial decision and usually involves amounts below some threshold, the policy wording is generally mute on such issues which works in your favour. In these cases, the insurance company can just as well carry the excess and any demurrage claims as well. As i've said, ive had success with such arguiments in the past but always, always, read the policy wording before making the claim and be prepared to push back when/if your own insurance company plays hardball.
* not sure what would happen if you only had 3rd party property insurance... whether the policy wording would allow you to claim the repairs against your insurance where the insurance company can recover costs from the identified at fault party... as always rtf policy book (pds)...