Neiski not with a 4 year old, if your child was a few years older I would recommend an adult one that you could set up but 4 year olds as you know are wrecking machines... don't think the screen on a fire or nexus 7 would stand up to getting dropped or anything.
What I would do in your position is buy a cheapo tablet and get a case and screen protector on it and download a parental control app... then buy yourself a Nexus 7 or Kindle Fire HD
