This same question was asked about Cam Newton in another thread. For Newton, I'd cough up two 1sts in a heartbeat. For Carr? It's hard to say what I'd be willing to part with. He seems to be a talented young QB with a bright future, but it's hard to really say what he'll become based solely on his rookie year.
I'd probably give up our 1st. That, or our 2nd and a conditional 2nd or 3rd in 2016 (depending if he starts 16 games and posts certain numbers, maybe 20 TD's and over 3K yards with under 15 picks). I think it'd be worth the gamble. He's done well on a terrible team, so he should do even better with a nice supporting cast here in STL.