Although Steven Spielberg passed on directing this as a feature film, he would frequently suggest story ideas to the original writing staff. The teaser of the Season One episode "Make of Two Hearts", where the ER staff rallies to save a dog, was written by Lydia Woodward after Spielberg's consistent suggestions to "do something with a dog".
If you recognize the little girl, Tatiana she would later go on to play the character Lily Adams in the AT&T commercials. Her name is Milana Vayntrub, and she is from Uzbekistan and would likely know how to speak Russian.
Carol Hathaway says her mother is Russian. In fact, actress Julianna Margulies does have some Russian ancestry; though the actress who plays her mother on E.R., Giorgiana Tarjan, is Hungarian.