Unreasonable to expect it, possibly not unreasonable to ask if its possible, definitely unreasonable to be pissed off if the answer is no.
Canine professional hat on - this is NOT the time to work on your childs phobia, nor is it the way to work on it.
IF your friend wants to help with this phobia you'll need to ask, ensure their dog can cope with whats necessary (being shut out of a room witha babygate, being in a room on a lead with a child far away, potentially sudden screaming or sudden unpredictable movement from child)...
They could send you a photo of the dog for you to use and show your child and talk with them about the dog.
If you live near enough then the next thing might involve short visits to huge open spaces where the dog will appear in the distance and you can follow them and talk about the dog...
Then similar but in smaller spaces
Thne possibly in their home using gates to separate dog and child
Then possibly in the same room.
I think realistically you would be FAR better finding a dog trainer who runs classes to help you with habituating your child to the presence of dogs as they are far more likely to have access to suitable dogs, sufficient dogs for your child to generalise and understand how to do this safely!