It's unlikely that rooting alone would stop your phone crashing. It's changing ROMs, e.g. to a custom ROM or stock ROM, that would (or should) solve the problem.
However, before going down that road, there are a few things to try to see if you can solve things on your current set-up.
First, try a soft reset, Power off phone > Remove battery for 30 seconds > Replace battery and power on.
If you're using an app killer, try getting rid of that, as that can be the cause of crashes. Let Android look after itself.
Check to see if there are any processes or rogue apps hogging your system. Menu > Settings > Applications > Running services > And check to see if there are any there that shouldn't really be there or are trying to start.
Check your phone for viruses, malware, etc.
Finally, try a factory reset. If your system is still crashing after a factory reset, then, either return it to Orange for a replacement or look at rooting/Gold card, which will invalidate your warranty unless you can get your phone back to how it was.