Again, I do not really feel you are at any kind of great risk taking your daughter (unless you're visibly a bad parent
...unlikely! ). I would be more concerned with the attention you can give to her while you are doing this business called adoption, especially for someone so young. There may be times when you'll need/want child care, too.
Regardless, you really should register with the US State Department when you travel. Since your daughter holds dual-citizenship and has a US passport, you can register her at the same time. Just remember that you must also have her Russian passport with you as for entry into, travel within and exit from Russia, she is considered by the Russian government as a Russian citizen and not a US Citizen. (And you need her US passport for exit and entry into the US)