Why is that little girl awake?

Maybe I missed it in the goofs section, but this is the one thing that has always bugged me.

The light's gonna blow at midnight, right? And J and K go to K's old apartment at around 11:30 at night (hence J's talk about getting to loving and cherishing quickly and the little girl can stay up as late as she wants, eat ice cream, etc).

Why was this little girl up at nearly midnight, and on what channel does Martha Stewart appear at 11:30 at night?