What bothers me is not how young the children are, but how old they are in the TV series. There is a trend among fantasy novels to make young children do things that are not meant to be done by such young children, and many novels/series are worse than GOT in that respect. At least in GOT its mostly some charisma or character of the children, and that's partially explainable by the fact that you get married at puberty and have to know how to act as a head (or any other notable position) of the household. Noble boys are also taught how to lead people, so by puberty they would have some idea, even if not that much experience. Compare that to children of 9-15 years old who do
physically impossible things. My siblings have recently been reading the City of Bones series and Percy Jackson series, both of which I have read, which reminds me once again about how these little children get to rule their world at least in part due to physical feats that are simply not performed by children. And in the Percy Jackson movie, the 12-year-olds look 17. Just like in GOT.
'Nough said.
(If I ranted away without being clear on what I'm saying, it doesn't bother me as much, but I agree that the children are a bit too grown up, but that's not as big of a deal in GOT as it is in some other books. What really bothers me is the movie adaptations.)