Course you could use for a new character but that too is pretty silly response due to the cap of only two Fed characters. Basically it means only one character will use the pre-order item ... your alt.
You can have three Federation characters. You unlock a third slot at level 6 for Klingons, but you don't actually have to use it for a Klingon. You can make three Federation characters.
Of course, that means you won't have a Klingon.
To the OP:- the bonus ship can be claimed by ALL of your characters. If you make two Federation characters, both of your characters can claim their own TOS Constitution. And any future characters you make will get a Constitution too.