My thought is you are a musician and your first job is to serve the song, or more specifically, the arrangement. If the music requires day a D below that low E, it’s going to sound odd playing it an octave higher.
As for drop tuning, there are a couple of options, if a significant amount of the music requires notes below E, as a lot of music written after the turn of the century does, you can try to get by with a drop tuner, (I’ll have further comments about this option later), adopt BEAD tuning (of which you give up a corresponding amount of the upper range of the instrument), or buy a 5 string.
If I were starting to play today, I’d buy a 5 string. Most music calls for it and for the most part it’s the standard range for the bass instrument. I have decent size hands, but for someone with small hands can be a challenge to master.
Drop tuning is a way to get some of those extra notes, but requires some mental adjustment. I played with E string in Drop D exclusively for 5 years before switching back to standard tuning when I bought a 5 string. Muscle memory doesn’t forget or give up easily. It took me months to retrain, but others seem to have no problem switching back and forth.
I think BEAD might be an option as you don’t need a new bass, although the bass many need a set up. You will need a different set of strings and they are going to be a bit thicker.
One last point, if she is thinking she may want to play in a school band, I would consult the band director as to what she would need in the way of an instrument range wise.
