I need to cut some carbon sheet. In the past I have used my bandsaw but found that one cut pretty much destroys the blade.

I need to shape the plate to the outline of a profile fuselage, so we're talking about cutting many inches. Plate is something like .045" thick, or perhaps a bit thicker.

Any tips for how to cut this stuff?

I used a coping saw, and tossed the blade when I was done.  You may need to use a few blades to cut that out.

It may be less complicated to get some cloth and vacuum-bag it onto the fuselage, instead of trying to get already-made stuff.

     I use regular ~1/8  HSS drills.  They will get dull but you can get many holes before any serious damage.  No need for carbide, CF is so abrasive the carbide is not cost effective in this application.  I sharpen my drills as long as the margin isn't too bad.  Leave about 1/4" between holes and connect the dots with a Dremel abrasive disc.  After that it's a simple matter of a belt sander or drum sander or file or.... Of course, a dust mask is mandatory. 

     I also use my scroll saw.  As soon as the blade starts getting dull, put a piece of 1/4 balsa under the work piece exposing a fresh set of saw teeth.  It will get dull again.  Do the same thing with 1/2 balsa or another piece of 1/4.  Kind of like shark teeth in many rows.  You can cut quite a while like this, then of course, the blade is toast.

I use diamond blades for my table saw for straight cuts.  Abrasive wheels work almost as well:10" ones for the table saw for long cuts, the Dremel 420 or 409 wheels for short ones.  Tidy it up with a sanding drum, disk sander, or belt sander. 

However, David's idea sounds good, and I intend to copy it.

Through-hole man trapped in a surface-mount world.