Ok. Kach, if you are a member of the Empire, you can just assume you already have a ship under your command.
Though
within reason!, flying around space in a personalised Deathstar, (no matter how cool), is not considered common sense or at the very least fair.
In otherwords, you do not have to build anything in realtime in any shipyards anywhere.
You want a ship, RP yourself having one! thats it! As long as it would be 'realistic' for your character to have one, then its not a problem.
Shipyards do of course exist , but purely in character, as a plot device.
Of course again, if you wish to RP yourself overseeing construction of your new ship , then taking it for its maiden voyage, thats even better.
I hope that makes things more clear.