Section 8 housing portability question?

im moving out of topeka, and porting my section 8 to kc missouri i have till the end of may to be out of my house does anyone know, or might have and, idea? of how long this process may take, because i dont wanna be left out in the cold with my children at the end of the month, if anyone?..has been in this situation..or knows more about this process?.. can you give me your best answer please help..thanks