I carry my passport, driving licence in a body bag around my waist. You can pick similar ones up at the airport.
In Torrevieja you can take your passport to any copy shop and they will copy and laminate it for 3e. I use the one in the road opposite the church square, I think Atlas is one the corner, the copy shop is just down from the coffee shop on the right.
Friends had their hand luggage stolen at Pisa airport whilst waiting for their flight. She was able to get back into UK showing this passport copy. He had to pass a more stringent check as all he had was the slip of paper from Ryanair.
Some people have reported that when stopped by Traffico copies of passport etc was acceptable on the understanding that they took the originals to the local police station. Depends how good your Spanish is, if Traffico aren't happy with your documentation then I believe the car will be towed away until you can prove who you are and that you are legally able to drive.
Don't forget you need to carry photo identification with you at all times. Also if driving and you wear glasses you must have a second pair with you, it's the law and you could be fined if you don't conform.