At what age do babies develop cat allergies?

My nephew is 20 weeks old, his dad is very allergic to cats and so are many members of his family.

My nephew has been around my cats pretty much weekly since he was born and shows no signs yet of being allergic.

Today he was rubbing his face in Demetri's side and licked him

I saw a study once (no idea how accurate) on one of those "what's good for you" tv shows that said that if a child or baby was exposed to something at a certain age, when their immunities were barely developed properly, they would have a better chance at being immune to the thing they were exposed to... if that makes sense.
I know nothing about this stuff, so it might not be accurate at all, but it does sort of make sense?

Yeah makes sense That's what we were wondering too, if he's around them often and being so young he may be okay.

I don't even know if you inherit allergies, but with it being in the dads family my sisters been testing the baby by bringing him round to play with the cats. It's funny, everytime they meow he talks back to them.