I was still finding it very difficult to stick to the "have got" system in our second class. I had a table full of plastic vegetables and pictures of animals, and I constantly found myself saying "Do you have a carrot?", "Do you have a cat?" and then having to rephrase it as "Have you got.....?" It felt very unnatural, even though, as I said before, if I was speaking to another native speaker, I would actually automatically say "Have you got a cat?"
He's definitely too young for me to simply wait until I'm pretty sure he's cracked "to have got" and then introduce "to have" and expect him to understand that they're exactly the same thing, but with a different form (from have got) in the negative and interrogative, as well as in the past/future!