Just a note on what it would actually take to manufacture a new ship, as some of you seem to be vastly underestimating the level of effort involved.
From laying the keel to commissioning, an Arleigh Burke class destroyer take 10 months of work by hundreds of workers to build. That's using a proven design, with known technology, and components that are built off-site for assembly on-site (e.g., radar systems, weapons systems, etc.). That's also using a construction slip that is already setup to build destroyers. The time for the first of the class, from contract signing to deployment, was closer to four years. Now, admittedly, the destroyer mentioned is about 200 feet longer than the fictional Firefly-class transport, but a U.S. Navy destroyer doesn't have to function in outer space. It doesn't have life support systems to provide atmosphere and artificial gravity. It doesn't have external radiation shielding or insulation against vacuum. It doesn't have defensive shields (much as the Navy might appreciate having them) or multiple drive systems for FTL vs. STL in space vs. STL in atmosphere. What do you have to have to put a real destroyer together? Apart from the hull, you have sensors (radar and sonar), communications suites, command and control systems, power plant and engines, weapons systems, emergency systems (e.g., fire suppression, life boats), internal fittings for crew such as food prep, plumbing, places to sleep, etc., storage for food, fresh water, fuel and munitions.
My point to this is that creating a new ship takes a LOT of time, a LOT of effort by many people, and in the real world, quite a bit of money. Each Arleigh Burke costs the US government about 1.8 billion dollars.
Now, the Family and the DWU have massive advantages over the IRL U.S. government in terms of free construction materials, tinker tech, super strength, etc. It wouldn't take them that much time or money to build their own IRL destroyer, but even pulling in labor from the DWU, it would easily take more than a year. My guess is that a reasonable time for them to design and build their own spaceship from scratch is at least 18 months, given all of their bullshit superpower advantages.