I wouldn't worry too much about the 11.75's. I seriously doubt you'd have any issues with them on an autoX course. Too slow, not enough consecutive laps (usually). I've been running the 11.75's on my Challenger for years now without any problems.
Road course or trackdays would be a little different. It would depend on the layout of the track and the number of laps you got to run. On a brake heavy course I'm sure you could get them to fade if you got to run for awhile.
Not saying the 13's aren't great, they are and I love 'em, but I don't think they're a mandatory upgrade to get started if you've already got 11.75's.
