It Has A Child card - do you stay in Tokyo?
It Has a Child doesn't prevent you from being eliminated. If it did, it would be phrased

If you would be eliminated, instead ...

instead of

If you are eliminated, ...

This means that other effects that occur on elimination still occur. Specifically,

If you are eliminated by an attack on Tokyo, the Monster who attacked you automatically takes control of Tokyo.
Warning: A Discard card that deals damage to you is not an attack.
If you are eliminated by such a card (Discard card), nobody takes your place, and Tokyo becomes unoccupied.

What it does is allow is for you to join the game with a fresh character. As usual, players start the game outside of Tokyo.

By the way, BGG arrived at the same conclusion.