We live in this one bed apartment for almost 2 years, I want to move to 2 bed apts because we are now 4 people, But I didn't find the right place yet, Do I have the right to stay until I find the place or What?

Can you ask your landlord if you can go month to month until you find somewhere?

What does your lease say, normally it converts to a month to month rental ( often at a higher price)