As mentioned in the other answers, the idea of "quantum teleportation" isn't really applicable to your idea as presented. However, if you are willing to do a different handwave, then maybe a solution might (or might not) appear.
One of the elements of quantum physics is known as the "wave function collapse". Short form is things don't "happen" until an external observer observes the event and the wave function collapses into its final form. One example of this is the Schrödinger's cat thought experiment, where the cat is neither dead or alive until someone actually looks inside the box.
Many people believe Schodinger didn't want to clean the litter box....
Since quantum physics is based on probabilities, you can think of things as happening because they are more or less probable than alternative courses of events. Going deeper, even improbable events can happen, but the probability of such things happening (like walking through a wall) is extremely low. The all powerful quantum computers in the scenario could be programmed to "look" for extremely low probability events happening, and "observe" them, making them come into being in actuality.
So the spacecraft is here, but you need to be there. If that is the case, the probability of the spacecraft (complete) being there is a very small but finite number. The computers being "looking" for that very small but finite event happening and "observe" it, bringing the ship into being at the destination.
While this sounds remarkable, it isn't forbidden by the laws of physics as we know them today. Observing a particular rabbit being in a particular hat at a particular time would be a trivial example of using it in a more mundane fashion, although what we would think of as "trivial" would probably require massive amounts of computer and sensor power and literally god-like ability to observe reality. The downside of this method of travel is it is "fuzzy". While there is a finite probability of the ship appearing at point "X" at time "Y", there are also probabilities of the ship appearing at slightly different places and at slightly different times. Moving farther away from the destination point, the ship itself and the crew might also be subtly or wildly different from the one at the starting point. This would be somewhat akin to a probability cloud surrounding the desired point in space and time, so events of similar probabilities could happen instead, and even events of greater or lesser probability might occur, with the events of greater probability happening more frequently. The ship appears, but Spock has a beard. A ship appears, but it is powered by a Dodge "slant 6" motor rather than the 440 "Hemi" it had at the starting point.
A fun filled version of this idea was done by Douglas Adams in the Hitchhikers Guide series of books, movies, TV and radio adaptations, as the "Heart of Gold", powered by the "Infinite improbability Drive"