Do parakeets got to have a different cage for mating?

No, you just need to buy or make a nesting box for them. A nesting box is some sort of covered box with enough space for the birds to move around in, it connects to the cage through a hole near the top, but it has to be big enough that the birds can get in. Also, to be able to check in once and a while without disturbing the occupant too much, make sure that the top can open up so that you can see in.

The one thing that is absolutely necessary though is nesting material (like strips of shredded paper).