Cooper is an experienced Engineer and Pilot who used to fly for Nasa, and Murph has picked up on his interest in science and engineering. This is shown by her interest in the moon landing book, which she defends even to the point of fighting at school where she is ridiculed for believing they really happened.
You compare the encoding schemes of Morse Code to the Enigma Cypher. While they are both ways of encoding data, they are of course totally different in their intention. Morse code is a very simple scheme of substituting patterns of dots and dashes for letters and to be easily learned and understood, the Enigma cypher is designed to completely obscure the meaning of the message by imposing on it an apparently random pattern. The skills required to 'break' the codes are totally different.
I don't remember (or its not said) how the 'STAY' message was encoded, whether it was Morse or the binary code that was used to communicate the coordinates of the facility. However if it was the binary code, by the time Murph works it out she'd already seen the example of the encoding of the coordinates when Cooper decodes it. So she was able to apply the same technique to the pattern of books pushed off the shelves. Yes binary encodes numbers, but in various ways numbers can be mapped to letters, such as A=1, B=2 etc. An intelligent girl puzzling over the meaning of the books would be motivated to try to work this out.