Firstly I am sorry to hear about your daughter and her experiance, definatly not what anyone wants to hear about and mistakes do happen but they can be deadly.

So what you have is a claim for compensation for injury and it's assumed Emirates accept liability in this case (it's hard not to). If it was a Personal Injury Claim in the UK against a restaurant, you would expect it to fit under the minor injuries in the sense full recovery within 7 day's and therefore it would have an award of a few hundred pounds so at most £500.

EK's proposal is 25,000 Miles which if you were to buy it seems they would cost £587 however if you were to redeem, Im sure you would get poor value. Unless your planning on using them towards a flight, I would personally reply, I note your offer of 25K Miles, I would ask you to provide the cash value of the points as points are no use to a 10 year old child.