If your pet currently gives a card, when you look up your pet in the pet profile tag, you will see a picture of the card on the upper right hand side of the page. There's a box there that is distinctly card shaped.
There are a couple ways to determine if your pet will get a card sometime during it's life; When you first get the pet, if you mouse over the pet drop notice (left hand side of your screen), it will give the pet's stats, and when and if it gets a card.
If you missed this popup, I would suggest using wizard101central or wizard 101 wiki to look up your pet.
Keep in mind, there is a pet talent that will give a pet an additional card. I've only seen it on a couple burnzillas I've trained, but I suspect it is likely something that exists accross the board, but is very rare, like pet casting.
When I want to know if a pet gives a card at Adult, Ancient, or even Epic, I equip the pet and then compare it to someone elses pet that is on my friends list or someone that i just happened to pass in the street.
(its kind of long srry) Yea heres how you tell if you pet will ever give you a card... other than from some really rare ability. Just equip the pet and click on another wizard 101 player in the game and view their equipment. (Note: they have to have a pet equiped too) move your mouse over to the pet icon and it will show you a comparison of your and their pet. If a card apperars in the side by side comparison then your pet will give you that card and it should say at what period (baby epic etc) your pet will give the card. If there is no card present in the comparison and on your pets side then you pet will not give you a card.