now
const T QMap::operator[](const Key&) const

Why not
const T& QMap::operator[](const Key&) const

every time copy constructor for T called just because QMap is const.

I read code.
>return T();

so may be throwing exception (QList - like) would be beter choise.

or something like
const T& QMap::globalInvalid()
{
static T invalid();
return invalid;
}