How long did it take you?
by the way. What do I have to do to get another ship? Still flying around with my Custom Miranda, the USS Atlantis.
You have to reach Lt. Commander rank.
Once you do that, go to Earth Spacedock for a chat with the admiral, then to the shipyard section and to the turbolift above it in order to requisition a new ship of your choosing (I got to pick it for 1 energy credit as a reward for reaching the rank in question ... my theory is that you will likely get the same thing).
So you can pick between 3 categories: Cruiser, Escort and Science (you can check out the various ships in the displays and info on each class before you make your choice though), and your desired career does not limit you to the class of ships you can choose.