Should I be worried if my daughter is her own imaginary friend?

Today Gigi runs into the bathroom and slaps me on the back of the legs then says, "Don't hit my mommy!" Then she says to me, "Gigi hit you!" I said, "Oh, you hit me?" Gigi says "No she did!" (pointing to herself). So I say, "Gigi hit me, but it wasn't you?" "Yes" she says. Then she whispers to herself, "Tell mommy you're sorry, Gigi." And then she turns to me, pats me on the arm and says, "Sorry mommy." WTW?!

If you're wondering what happened to the spider...

I think we bothered it too much and one day, it was gone. But then, we found a much smaller one under Gigi's window! I decided to leave that one alone.