Problems seldom go away and you won't have much time to solve them. If you decide to go ahead with a clutch or two and do so responsibly, you will undoubtedly learn a lot. You may enjoy it so much that you, like so many before you, will make the transition from pet owner to breeder. It's possible you don't want to devote the time, energy and money required to properly support your bird's reproductive activities. Your birds won't suffer if not allowed to raise babies.
Many pets live together and copulate regularly for years.
Unwanted eggs can be disposed of but you will need to learn how to control the hen's egg laying to protect her health. Your avian vet can advise you. I apologize for such a grim column, after all, pets are kept for pleasure. These casual breedings have caused so much grief to the pet owners and suffering to innocent baby birds that I must encourage people to either commit to doing it right or not doing it at all . Allowing your pets to have babies IS fun, it IS easy and it DOES take extra care, knowledge and money.