I think saxophone would be too big for your DD.
Alto is the 'normal' size that you see played in wind/jazz bands, but it's really quite big and heavy.
DS1 who is 10, big for his age, and now 5ft, started learning Alto sax last year and found it heavy. I play too, and still find it makes my neck/hands ache after holding it and standing.
Good advice about learning the clarinet, and then moving onto sax (which is what I did...).
But I see you said,
"DD2 plays clarinet.
So I'd like something different for DD3."
Perhaps, more importantly, you need to ask your daughter what she'd like to play? She needs to be enthusiastic, and want to play whatever she learns.
Personally I'm a big fan of young kids learning to play the recorder properly. It IS a proper woodwind instrument, and can really be quite beautiful when played well... (look up Piers Adams...!)
Learning to read music on any instrument will help any future instruments, and the descant & tenor recorders use the same fingering as a saxophone.
Otherwise, what about the oboe? Smaller than a sax, and always in demand in orchestras (whereas flute/clarinets are ten a penny!)