Vet rewards are account based. Meaning that what matters is the accoutn age, and not he character age. If you can use a Vet Robe/Ethy/etc., and create a new character, they will be able to use the vet robe/ethy/etc.
Any character on the account can claim the reward, and they can be traded among your characters. Just be carefull that when you delete a character, they are not wearing or have in their pack or bankbox anything you want to keep (gold, rewards, items) because you will not be able to recover them.