If you have access to $G$ through an oracle, then you have a random permutation oracle, which is the usual way of modeling an idealized one-way permutation. In particular, it is therefore a one-way function.
As pointed out by fgrieu, however, a random one-way permutation is not hiding in general. The natural game to capture the hiding property of some primitive $P$ is as follows: the adversary picks $(x_0,x_1)$ arbitrarily, and sends them to you. Then, you pick a random bit $b$ and return $P(x_b)$; the adversary wins if he finds $b$. A scheme $P$ is hiding if the winning probability of the adversary is negligibly close to $1/2$.
Of course, a random permutation does not satisfy this: as long as the adversary sends different values, he can always compute $G(x_0), G(x_1)$ himself, and check which one is the value he got from you. In general, a deterministic function cannot be hiding.
It is possible, however, to construct a provably secure hiding commitment scheme from a one-way permutation - in your case, it will be perfectly hiding, since you have access to an ideal random permutation. The standard construction goes through the Goldreich-Levin theorem, that shows how to extract a "harcore bit" from the one-way permutation, such that finding this hardcore bit is as hard as inverting the permutation, and uses this hardcore bit to mask the bit you want to commit to (there is a Wikipedia entry about this construction).