Child Trailer - Safety

I am getting interested and excited about different ways of taking my little one around on the bike. One of the options is obviously the trailers that look like little Wendy tents on wheels, with a big flag sticking up. I quite like these but my other half fears that they will be instant death for the infant occupant. She is convinced that they are invisible and will be run over by a large truck or similar.

I am wondering if anyone has any information about them and their safety; preferably evidential but anecdotes are useful too. I would be particularly interested in seeing any figures for accidents involving such trailers (Oliver?).

I've tootled my kids the mile and a half to school in one of these trailers for three years without incident. The only reason I've just stopped is because they're now 6 and 8 years old and I can't wedge them in anymore, especially not in their winter coats.
That and the 12% gradient pulling 10 stone of children and trailer on singlespeed...

Go for it!