As BA crew (and former Qatar Airways too) I can confirm that you should not have been given an extension seat belt under any circumstances if your child was over the age of 2.
As Jetsetlady said, if you were to adopt the brace position for any reason regardless of whether there was an impact or not you could cause severe and possibly permanent damage to your childs still developing body.
What you heard from the BA crew member on your last flight may not have been what you wanted to hear but it was the right thing, the previous crew member was in the wrong and clearly does not read their memos as this is a subject we get reminded about over and over again! lol!