Don't feel too bad, this sort of thing happens. I'd say apologize to your neighbour, explain how it happened, and tell them the steps you're taking to deal with the issue. Beyond that, no need to do anything. They'll likely appreciate knowing that you're handling the situation.

I sympathize with you, I honestly do-- it sucks to have a big responsibility unexpectedly dropped on your lap for an indeterminate amount of time.

But in this case, yes, I think it would be unkind to ask her to find someone else. Your friend is in a scary and stressful situation. Don't give her one additional thing to stress about. You are doing something really helpful for her and I am sure she appreciates it. Suffer through the next few days-- they will be over soon-- give the dog back, and then celebrate.

All this being said, can you hire someone to take the dog on some long, LONG walks for the next few days? Lol.