First, about the steerer tube extension (the piece with the QR at the bottom). There's a slit at the bottom to allow it to be tightened onto the forks - at the top of that slit it widens into a hole. My steerer cracked from that point, horizontally round the tube. If you want to use the seat - I would check the steerer tube regularly for cracks developing (I think it would develop gradually).
Since then I changed to non-QR steerer extensions but then the folk steerer cracked right off, just below where the extension tube clamps on, just above the top head race of the headtube. The fork steerer tube is much thicker than the QR extension tube and I don't understand how it could crack so perhaps this failure is a lot less likely to happen for you.
I think they are making the steerer tubes a bit thicker now since I bought mine, but I would still say that it's not designed to handle the weight of a loaded child seat. The fork steerer tube should not have broken. The only thing I would say that might make this less likely for you is that in the couple of years up to my breakages, I was using the swift heavily for standing starts (I do track racing) and these put huge amounts of sideways torque through the bars and steerer, much more than you get in a sprint. So if you have been riding gently up to now you may be OK, but I wouldn't put my kid on the bars.