When is a good time to upgrade to a full frame, and is it even necessary?

if your camera does everything you need it to do, you do not need another camera ...
i'd suggest you use your existing camera to its technical limits and consider what you need from there ... maybe you like all the low-light photos you take at concerts ... perhaps you realize you need off-camera flash setup? or a faster/wider/longer lens? any of those are usually cheaper than a new body ...

per dxomark, the ISO performance difference between the d600 and d5100 is about 1 stop ... about double the shutter speed for 3 times the price ... and that's not even considering the lenses you'd have to buy to match your current set-up ...
and what if you wanted to photograph distant objects? a ~1200mm p&s costs $500 but a 800mm lens and extender for a full-frame body cost $15-20k ...

maybe if you went into portrait-type photography, a larger format would make more sense ... but i don't see the absolute need based on what you're saying ...

hope this helps ...