You should describe all your daughter's difficulties against the PIP criteria. Regarding the possibility of an assessment, you should write about your daughter's difficulties and request a paper-based assessment - as it would cause her "overwhelming psychological distress to be spoken to. You can say if they need further information, they can speak to you as her appointee.
If, for some reason, they send out a letter for a telephone assessment - check that you can do the talking or send in an appeal that you want it to be a paper-based decision.
BIS
Nothing on this board constitutes legal advice - always consult a professional about specific problems