Having watched my wife fall off her bike with our daughter on the back in the seat (chain dropped off the front rings causing a stall), i will not put her in her seat without a helmet.
The seat (hamax) was brilliant, the bike went over and my daughter was well secured within it, but her head did fall to the side, and if she were the size she is now (it happened last summer) she would have banged her head on the tarmac.
If she were in a trailer i would not be so worried, neither am i when she is playing around, but in the seat she is in a fixed harness and therefore more likely to bang her head.