Sarah - please try not to worry about the meeting with the CAFCASS guy. He should know that when dealing with young children they won't get anywhere unless they put them at their ease and he should do sticking/colouring with her really or play with her toys with her, so that it takes her mind off being talked to by a stranger. ideally there should be more than one visit but CAFCASS are very under resourced especially since the rise in care proceedings since the Baby P case, so he may just do it in one visit.
He will need to see your little girl by herself but with you nearby. It's just that he needs to be sure that she is not just saying things to please you. I realise this is not the case, but believe me it can often be the case. Also many mothers do try to turntheir kids off fathers, sometimes with good reason so CAFCASS workers need to be sure this isn't the case.
I would not really expect that your little girl will say vry much to a stranger, unless he is very skilled. Children should not be asked direct questions "do you want to see your daddy" etc but their feelings should be elicited through playing and drawing etc.
It's a great pity your daughter has become stressed over this meeting, this should not happen. She will also be picking up on your anxiety so you need to take care over that. Presumably you know the reason your daughter does not want to see her father. You don't give any background info - i.e. when was the last contact and do you trust him to take proper careof her and is he reliable and trustworthy.
In your meeting with the CAFCASS guy try not to become over emotional. The thing is they have to go by the law and if you are married or your P has Parental Responsibility you have equal rights to a child. the child's wishes and feelings do have to be taken into account however. Don't rush ahead to worrying about taking your daughter to contact "kicking an screaming" as this is unlikely to happen. It maybe that contact begins at a Contact Centre and willneed to be monitored to ensure that it is meeting the child's needs.
The CAFCASS guy will have to write a report so he will almost certainly want to make a few notes while he is with you. You have a right to see and comment upon any report that is written about you.
Hope all goes well for you