I want to prove the following:

the set of all intervals with rational end points is countable

I know rational numbers are countable, so there is a a function f: N x N -> Q x Q.

With this, i could say that since the naturals are also countable N -> N x N, then there is a function g: N -> Q x Q

Is this right? I am sure this is a not a complete proof, so if somebody could provide some help.

Thanks