The velocity required to fly from Mojave to Queensland, Australia (some 11,600 kilometers according to one of the comments, which is further than NY to Tokyo) is very close to that required to achieve orbit. The difference between an ICBM's peak velocity and orbital velocity is quite small. That's why several former ICBMs and even some IRBMs became orbital launch vehicles (Thor, Atlas, Titan II, R-4, etc). The biggest difference is the trajectory. An ICBM tends to fly a higher trajectory than most space launches.

Also, flying from California to Australia would require a retrograde launch, taking considerably more energy than going in the other direction. If you had a vehicle capable of making that trip with any kind of payload, it could easily be an orbital vehicle.