You'll need to bring the SRT-6 Kompressor ECU with, and probably the paired keys unless you want to do some reprogramming shenanigans.

If you have a 6-speed, it's probably not worth it as you'll either have to fabricate a nonexistant adapter or get a different crankshaft to mate the transmission, and nobody's gotten the ECU to cooperate as far as I know. Search the forum for posts by HDDP and you'll find a description of how it's done with a custom third-party ECU (and a lot of money).

The rear end on the Limited differs from that on the SRT so if you'd like the same gearing, bring the rear diff along as well.

The SRT also has different shocks, springs, and brakes if you're going for the full SRT build.

"CrossfireKat" put an SRT-6 engine in a limited with the minimal swap (ECU, engine) and it supposedly works, so it's definitely a possibility. But then you have an SRT-6 without good brakes or shocks, stiff springs, or the slightly higher rear end.

In short: you might as well buy an SRT-6.