Dr Bernstein is very popular with some T1s but I'm not sure how popular his ideas are with diabetic teams managing T1 children. I'd personally hesitate to put a T1 child on a very restrictive diet, specially as the advent of modern technology, in my opinion, gives more dietary freedom. Though the low carb approach is very popular on these forums, that is partly because of the low carbing T2 community here, which I suspect feeds through to encouraging low carbing T1s to post here.
Just my opinion, but I think you'd want to be on good terms with the diabetic team managing your child's levels, so listen to their advice. I've also seen dietary advice for T1s change a bit over my lifetime. Whatever happens, you and your child will probably need to learn to count carbs (5's probably a bit too young but I was doing it at 8). The only thing I remember eating differently from friends is that we didn't have a whole lot of sweets/candy in the house, and it didn't occur to me that pocket money could be spent on sweets, and at Easter, where some friends got massive quantities of Easter eggs, I seemed to end up with a smaller egg and a toy ...
But I don't remember eating much differently from my non diabetic brother.
It may be worth your while also investigating the diabetes.org.uk forums of the UK diabetes charity, as they do a lot of work regarding T1 children.
I'm not personally convinced that a healthy diet for a T1 child is much different to a healthy diet for a non diabetic child.