It’s quite simple
db..find().forEach(function(d){ db.getSiblingDB(' ')[' '].insert(d); });
You can do a mongodump of a collection from one database and then mongorestore the collection to the other database.
I used robomongo and it a documents view, just used this query with the right names for collections and databases, I was able to copy around 3000 records in less than a second on my old Macbook air.