A deductible would not apply here. What would happen is that the other driver would make a claim against the physical damage liability portion of your policy. Your insurance would pay the entire $1,000.
The deductible comes into play if your car is damaged in a one-car accident by you or another driver hits you and does not have insurance. The deductible would come out of the amount your insurance company pays to repair your car using the collision coverage portion of your policy.