I am a long time MTT grinder on UB/AP. I've profited over 100k online. Here's my take on the situation.
You started the hand very deep, over 50 BB's. Always keep in mind how many BB's you have. Between 10-15 is a SS, 15-30 is a mid stack, and 30+ is considered a big stack.
That being said you were super deep to start the hand. You should be min raising or at most 3xing this button here with QQ. You want to make it look like you are trying to steal the pot with a min raise. Don't be afraid that you are giving good pot odds
to your opponents. REmember, you are super deep with a premium hand. Get used to 2xing, 2.5xing or 3xing all of your raises.
The only way I would ever ship in this spot is if i knew someone in the blinds was tilting and going to call super light, or if they are just a huge fish who donks off lots of chips.
All this said though, I'm never really getting away from my QQ here. It's just too strong of a hand. Unless I had a super solid read, which most of the time when you are playing online, you don't, I'm not getting away from the QQ. I consider it a cooler. Hope this helps.