Well you can do backup of all jb apps and hope that all of them are working after with iOS 6.1
First you would need to update iOS to 6.1 and in case that everything works out of box you will get possibility to do 6.1 backup after and which you will have everything like you have now with exception of apps that don't have 6.1 support, BUT!!
There is always but. You cannot restore 5.1 backup to 6.1 iOS, which means that you will in case of problems have to re install everything again, if you have backup of your apps in iTunes then it will be a bit easier, but still, you will have to re install everything.
Golden rule, if it's working, don't fix it.
First you would need to update iOS to 6.1 and in case that everything works out of box you will get possibility to do 6.1 backup after and which you will have everything like you have now with exception of apps that don't have 6.1 support, BUT!!
There is always but. You cannot restore 5.1 backup to 6.1 iOS, which means that you will in case of problems have to re install everything again, if you have backup of your apps in iTunes then it will be a bit easier, but still, you will have to re install everything.
Golden rule, if it's working, don't fix it.

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