I am an IBA rider also, but don't think that has anything to do with a skill level (sorry, I believe that most of the style if riding is the easy part of riding)
That said, my dad put me on the back of his bike when I was 3, and I have been addicted ever since, I got my first bike the next year for "christmas" (in May) and never looked back. In Kentucky there were no helmet laws then, and there might as well not be today.
If your child is old enough to maintain the focus needed to ride as a passenger, want to ride with you, and you have the funds to buy the VERY BEST in protective gear than by all means go for it. There is risk in everything, growing up we saw/knew a few kids who didn't grow up, the two I remember the most were a fall from a tree and playing HS baseball (line drive to the head). My future wife and I have decided to I will get to buy a Hack so that we can take the kid with us once he/she is old enough (we are thinking about 4 years old) then maybe around 6 or so throw them on the back if they want.
Racingwise, I have seen kids crash hard at junior level races and the parents never thought twice about the paramedics slicing off $5k in gear (no joke the EMT asked the dad if they should cut it off or slide it off to save money
) I also was at the track when a 12 year old died in a minor lowside.
I cannot stress this enough the following:
1) Gear, get the best and ATGATT, kids don't always know what they are getting into. It is your responsibility to mitigate the risk. My fiance didn't when I invited her to ride with me for the first time, but we went to some shops and found gear she liked that was at or near the best available.
2) Focus. My girl did a 2up ride with me on the track also, she loved it and learned alot about being a passenger and how much her movements effect the bike. Kids will not know this instinctively, you really should ensure your child has the focus and start with SHORT trips to the store, McDonald's, etc and work your way up.
3) The dangerous riding (at least IMHO) is traffic; the stop and go stuff in town, make sure you (30+ years you should) and your passenger know what to do. I would suggest a helmet to helmet communication system and if possible get one for your wife also and have her ride behind. You can communicate to your child and she can let you know if junior is loosing focus and may need a short break.
I don't have any kids, but I have been thinking about this stuff for a while now and look forward to the responses of others also.