Evy, I agree that your daughter's co-worker was presumptuous but at least she bought the fabric. I would do it--take the request as a compliment but I would stress that this was a one time deal (she may show up with fabric at Christmas and assume you'll make more).
As for the strap on a child's bag, I'd err on the side of caution and make the straps short, just like a handle, instead of a shoulder style strap. With all the litigious people out there you wouldn't want to be held responsible if the child had an accident due to a dangling bag or strap around her neck.
You're a sweet person to do this.