You don’t have to take the fighter first. It’s perfectly legal to take the carrier and leave the fighter stranded. In order for the fighter’s move to not be a suicide mission, the only requirement is that it have a possible place to land (assuming the defender never hits). Once the battle actually starts, it’s up to the owning player which casualties are taken.
The rules dealing with suicide missions address movement only. There is nothing in the rules that indicates that casualties must be taken in a certain order to preserve fighters’ landing spaces.
