No. Not even on their scooter around the block. Out the front where I could see them (here, not necessarily in all areas, yes, but not out of sight. By next summer, probably around the block (if no roads to cross) but these days not with a dog. Too many untrained ones, I'd be worried might attack ours, with the child scared & out at risk.
many years ago my friend was walking their small timid dog (she was about 7) and another dog attacked & killed her dog, she's in her 60's now & the trauma (understandably) never left her.
Explsin to your child that other people's dogs are too much of a risk, if she's pestering you to be allowed to do this alone.
Have you considered allowing her to do a class for some kind of training, or even just encouraging her to teach the dog to do a truck ir two? I presume you already allow her to hold the lead when you take the dog for a walk?!
or are you the one wanting her to do this so you don't need to go?