Translation:She is not putting up her umbrella.
No, you cannot say so in this context. 彼女の傘を差していません means 「の」is showing possession therefore it will mean '(Whoever the person) is not putting up HER umbrella.'
If there is this guy is putting up a lovely flower-patterned umbrella. Then his friends saw him. One friend asked, 'Is he putting up his GF's umbrella?' and the other friend replied, 'Nah, he is not putting up her umbrella but his own.' then 彼女の傘を is possible.