The one suggested by Eirene could be correct, but also note that the link she provided is to the work of aa copyist Chernakov (??). The original painting was done by Charles Burton Barber - A Special Pleader
. Here's a link to the Barber painting: http://www.historylink101.com/art/Famousab/barb564033.html
Or...it could be a work by Briton Riviere
- Compulsory Education (Naughty Boy). This painting was used in the Pears soap ads around 1909 - note it's sometimes attributed to Burton Barber (and called The Reading Lesson --but that's wrong).
here's a link:
If not, keep trying Burton Barber -- he did many paintings of little girls with dogs. Other artists who painted many "girls with dogs" are Arthur Elsley and Frederick Morgan.
All suggested artists enjoyed painting genre scenes (everyday life); they were all British and painted duriing the Victorian and/or Edwardian periods when girls and dogs were very popular.