Not sure about BASIC as a first learning language, but if she loves it and so do you, that's the main thing.
The actual language that you start with isn't as important as learning the various techniques and structures within programming. Some BASICs are better than others but if you learn properly, you will normally be able to switch between languages with little trouble.
For example, I started with Pascal rather than Basic and have mucked about with various shell scripts, COBOL, Python and a few more obscure languages that I doubt are in use anymore. Once you pick up the syntax, it's not that difficult.
It's what got me interested all those years ago.