When to transition into an ending I know the rule of thumb about trading pieces when you have a lead (and pawns when you're behind), but how does one decide an advantage is sufficient enough to transition into an ending by trading queens?  I've found that a small lead of a pawn or even a piece often isn't enough to win in that case.
There is no easy answer to that question. You need to be able to accurately assess your winning chances in the possible endgame and to do that you need some knowledge and a lot of experience. 

You can acquire the knowledge by looking at the basic theoretical endgames. That will tell you that two knights aren't enough for mate, that bishop and pawn might still be a draw, that rook and bishop vs rook or knight vs rook is tricky but a draw and many other things. 

For the experience you'll have to play. Then you will also notice that apart from winning chances, there is another factor to the decision of going into an endgame: Minimising the risk of losing. Often simplification decreases both: The chances of winning and the chances of losing. So if winning is more important to you: When in doubt, keep the queens.