In contrast to conventional internet where classical 1s and 0s are transmitted via some medium like copper or fiber optics or radio waves, qbit states are far too fragile to survive such transportation and so would be transmitted via the quantum teleportation protocol.
Physical networking infrastructure will still be necessary; teleporting a qbit requires a pre-existing entangled qbit pair in addition to two bits of classical information, so you'll need some method of sending one half of an entangled qbit pair to the recipient. It's okay if this process is lossy, because you can easily generate & re-send an entangled qbit if it gets lost. Once you successfully manage to get the entangled qbit through, you can use it to teleport the qbit you actually want to send (whose state is presumably the product of some long, expensive computation and therefore far too valuable to risk sending via such a lossy channel).