Everyone has a way to meet the need of a carrier group. I choose to equip mine with a construction ship. That way as the fighters are used up, I can replace them within a few turns local to my fleet. Then just do a transfer.
It works for me, but my play style is drastically differant than yours I suspect. Any who, good luck.
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"We've made too many compromises already, too many retreats! They invade our space and we fall back -- they assimilate entire worlds and we fall back! Not again! The line must be drawn here -- this far, no further! And I will make them pay for what they've done!" -- Patric Stewart as Captain Picard
UCP/TCO Ship Yards