no, you got something completely wrong there

first of all, the construction frigates belong only to the one planet they´re first built at (every planet has its own ones, which appear automatically once the planet is yours).

what you need to do is to colonize a planet (after clearing the environment of hostile ships), which can be done by a colonization frigate, or by one of your capital ships (the one in the middle when you build them). the colonization frigate can be built in a small shipyard without any prerequisites.

the research which requires 3 civ stations enables your ships to jump to another star system (or sun, if you so like)

construction frigates can NEVER jump, but are spawned at each planet after colonising it. jumping to another planet is a tech level 0 tech for all races ie all races constructed and trade/refinery(spawned from tradeport/refinery) ships can jump as needed(fighters & bombers can not jump because the ships they are attached to can).

to colonise another planet just take a colonising frigate(after killing the militia at the planet) OR cap(usually the middle cap) to the planet and colonise.

harpo