It may be difficult for your DD to do but keeping a detailed diary of her week might show how her symptoms are affecting her daily routine
It will be harder to get PIP if not on any current meds, as they can't seem to see past that.
Send in the referral to student counselling and a report from her counselor if possible. Send as many medical letters as possible - try and get her notes from GP or student drs as they will note how often she has needed to see then, referrals and notes regarding her admissions.
Send the copy of her autism assessment
Refill in the form adding any extra information to each section NB remember it has to be done safely, promptly and in a reasonable time frame to count as being actually able for her to do.
You can Google to find the law around the wording of what the actual pip legislation is.
Ask for the full report of the decision making and see why points were given or not. Look up the points given for each activity and be realistic as to if she is able to do these.
Don't lie or exaggerate but word your answers so there is no ambiguity. Repeat yourself. If she struggles with timing say....this may make it hard to make a meal....but then don't assume they will remember this point in a later question. Repeat, repeat, repeat
You can ask and I would almost guarantee be given an extension on a written appeal to gather as much evidence as you can.
Repetition and evidence are the keys I've found.