Did Molly Brown really survive a flood as an infant?

At the beginning of the 1964 film The Unsinkable Molly Brown, Molly Brown is seen surviving a flood in Colorado when she was six months old. Her cradle is seen floating down a rushing river and once it sinks, she walks on shore slowly and apparently unfazed, and she is eventually adopted by a farmer.

Is this a true story, and if so how did an infant like her get in a flood and did her parents drown in it?

Also, could an infant really survive a thing like that?