I am never looking to limp call with these hands. I may occasionally limp with AA or KK but never with QQ. After my limp I'm looking to call a shove, or re raise any raise that has occurred.
The main times I may do this are when expecting a crazy player to shove, or maybe someone has just lost a lot of chips and they are likely to shove, plus I am UTG/UTG+1. Or maybe its late stages and lots of players are short and there is a lot of shoving going on....a good time is just after bubble bursts, as players tend to have been holding on to get into the money.
However, all that said, these are very very rare occasions with specific table dynamics.