I can't answer the part on orthodontists (best to ask your dentist for a referral) but I had a huge gap between my front teeth and very large teeth as a kid.
My teeth looked proportioned and my gap grew together by middle school. My father had same teeth, and 1/2 my kids have same teeth.
My teen's gap has closed now, and his teeth look more proportioned now that his molars are coming in. He has somewhat crooked teeth but his bite is fine.
If we need to correct the crookedness, we were told to wait until more teeth come in.
Not sure if that helps, but we had a few school pictures with my kids smiling with mouths closed - so been there. If it's really bothering her though (my kids saw all our teeth were like that so weren't as worried) I would go see someone. If it's more involved, you'll want to know now.
Good luck :)