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.