I'm so sorry to hear what you've been through. Most appeal panels are used to distressing cases, and quite skilled in handling them sensitively.
I'd be surprised if they asked you much about your illness and treatment, provided you've submitted (or will be submitting) the medical evidence. Basically they need confirmation of the period over which you were affected. You could try and pre-empt any discussion by saying at the outset "I hope I've given you all the medical information you need as I do find it distressing to talk about the details of what I've been through."
Questions are more likely to focus on what signs there may have been of the impact on your daughter.
Secondly - and most crucially - they will want to see as much evidence as possible of academic ability (other than in the period July - December 2009), and you are dependent on the headteacher for most of this:http://www.elevenplusexams.co.uk/11plus ... rs.php#b11
Hope this helps, but do ask if you have any further questions.