Could I say instead of 'That's her' , 'She's her'?
I definitely wouldn't.
If you've already said 'She's...' before you realize you can't say '...her', you could say '...the one/the person/the girl...'
b
Native English TEFL student
The previous posts are of course quite correct, however there are certain idoms and sayings which would use 'she's her' such as, she's her own worst enemy and she's her own person.
One trains to be a teacher. During the period of training, one might be referred to as a trainee (teacher) or student (teacher).
Context is always important; labelling is rarely important.