You can't get CITES permits after the fact. The permits are issued for the purposes of import and/or export. What you should get, at the time of purchase, is a copy of the permit. And keep it, so that in the future, you could pass it along to others in the future if you sell the animal or offspring. And yes, the permits are for individual animals, though in practice, if something is really common, there is no real way to keep track of them all, as the individual animals are not marked and correlated with the permits.
If you can't get a copy of a CITES permit for any Appendix I specimen, I'd be leery of buying it. At least get a receipt to show that you purchased it here. That might help if you get into trouble.