While you can catch Nidoran (male and female) and evolve them into Nidorino and Nidorina respectively, you cannot evolve them further to Nidoking and Nidoqueen in Pokemon Emerald. These evolutions are exclusive to later generations.
You will need to transfer Nidorino and Nidorina to a later Pokemon game (like Diamond, Pearl, or Platinum) to evolve them using a Moon Stone.