Yes, to have kids you must be an adult.
To have kids with a partner you must be an adult.
You also have to have 4 hearts with eachother.
To check this:
Navigate to your friends icon, using the [ a ] button find the friend you want to eventually be a partner with, press the [ b ] button a few times. You will see a certain amount of hearts, or smiley faces.
To be partners, and have kids you must have 4 hearts with the Tamagotchi.
//Haze