I asked our pitching coach this when DD was in 10U. He thought 40 was a good rough estimate, and reaffirmed what you already would know in that it just depends on the pitcher, some need more, some need less. But he thought 40 would work for DD.
I think 15 minutes is about the average for all the pitchers I've seen over the years. I have no idea what the number of pitches would be as I haven't counted any, and they all have their different routines.
It is really dependent upon the kid. As the players get older, the number of warm up pitches needed goes down.
She needs to throw 20 or so to get loose. After that, she needs to get her "head right" and then get her pitches working. It is really up to the kid.
The best thing is to teach your DD how to play pitch and catch underhanded. One of the ways to use the skill for warm ups, so that she can get her arm loose and ready to go without needing a catcher in full gear.
Denny Tincher has an article on his site about wearing yourself out before you pitch. If you play 6 games in a tournament and warm up 6 times and then pitch. That's a lot of pitches. DD pitched in 3 games this weekend. Total of 10 innings and warmed up 4X. It was a two day tournament.