Having seen the clip, the idea that Rumple had been a lost boy himself didn’t even occur to me until someone else brought it up! When Rumple broke down in tears over the doll, I immediately assumed it had opened a fresh wound of the pain of loosing Bae. I don’t think Rumple was in NL as a child…I’m guessing he ended up there as the Dark One in an effort to get Baelfire back. I think he must have known he was there at some point. Maybe Bae *made* the doll while he was in Neverland if he didn’t have it on him. I just have a feeling it is connected to him. Here’s a thought- perhaps Rumple came to NL and then Baelfire found a way to escape and ended up in our world- we haven’t heard that story yet. Conversations in past episodes definitely suggest Rumple knew something of Bae’s whereabouts after he fell through the portal at some point.
Another reason I think it’s more likely that the doll has to do with Bae and not Rumple’s childhood is that it fits better with the story they are trying to tell rather than introduce a whole new backstory not directly related to the current situation. At any rate, even if he was there as a child, he had to have also been there as an adult after he became the Dark One since Felix refers to him as the Dark One. Also, if Pan and Rumple were enemies, I can’t imagine events leading to that happening when Rumple was just a kid.
However, as I always say, I have been wrong before!