The TVTropes Trope Finder is where you can come to ask questions like "Do we have this one?" and "What's the trope about...?" Trying to rediscover a long lost show or other medium but need a little help? Head to Media Finder and try your luck there. Want to propose a new trope? You should be over at You Know, That Thing Where.
Hm. Not quite, but definitely closer. I was thinking something like A Boy and His X but for girls.
The girl would probably qualify as a Fluffy Tamer.
I figured this trope was common enough that "Little girl with big daddy/monster guardian" would have its own page. I've seen it a lot recently on writing prompts, but assumed it had actual established works based off it. Maybe not. Hmm.
A Boy and His X can have female examples.
I actually just found this page which is super close... https://tvtropes.org/pmwiki/pmwiki.php/Main/OverprotectiveDad
You might also want to look at Little Guy, Big Buddy and The Kid with the Remote Control.
Oh, those are good ones, Synchronicity.
A trope I see a lot of but can't find anywhere on TV Tropes is simply about, say, a princess being given to a dragon to be eaten, only the dragon doesn't eat her and instead raises her. Or, in other variants, a little girl (sometimes boy) stumbles onto a dragon and befriends him.
I was wondering if this trope existed. If so, what is it called?
Examples: https://www.reddit.com/r/WritingPrompts/comments/8e7yif/wp_as_a_solitary_dragon_youve_spent_countless/
https://www.reddit.com/r/WritingPrompts/comments/7zrk9l/wp_a_dragon_fights_to_protect_its_most_valued/
https://www.reddit.com/r/WritingPrompts/comments/813gcd/wp_youre_a_powerful_dragon_that_lived_next_to_a/dv0auer/
Etc.