Presumably, you're just holding him in case your starter gets injured or for use in your starter's bye week.
I'd definitely hold on to QC if your starter has a bye in week 7 (when QC is @ Detroit).
I could go either way with Carter in week 9 (Washington), and week 10 (Buffalo).
I would not start QC next week (against Philly), week 8 (@ TB), or week 12 (Carolina).
And of course, if you have the room on your bench, it doesn't hurt to hold on to a guy who could prove valuable in a late-season trade or spot start.
Everything you know is wrong.