I'd send her over a basket of home-made muffins or cookies to welcome her to the neighborhood. Include a little card and lightly mention to her that you're aware that your little one is a barker, but that you're working on it
! I think a friendly move like that on your part will really make her feel like part of the neighborhood and less apt to complain.
Perhaps getting her dogs and your dog together for a play date will help, too!