It is interesting to compare Kezia with her sisters and how they treat the Doll's House. It is clear that for her sisters, the Doll's House becomes a valuable "chip" with which they can play and maintain their superiority in their society. However, perhaps Kezia wanted to rebel against this social segregation and share the light of the lamp - something that she has been attracted to since they first received the House - with others.
"The lamp's best of all," cried Kezia. She thought Isabel wasn't making half enough of the little lamp.
Clearly the light of the lamp can be said to operate symbolically in this tale, referring to the light of a world free from prejudice or class restraints (note Else's comment about the lamp at the end of the tale). Kezia wants to show and share the house with the Kelveys, and even asks if she can invite them round. However, she is refused without a proper explanation, only being told "You know quite well why not." Notice too that Kezia invites the Kelveys in immediately after the most savage bit of taunting that the girls make against the Kelveys - she clearly feels that the Kelveys are wronged and wishes to share the light of the lamp and the House with those who have little other "light" in their lives.