Hi Katie-lee,
Birds can lay eggs with or without a male, but the eggs will only be fertile if she has mated with a male. Most likely nothing will come from these eggs. First clutches usually fail anyway, and without a nest box, she may not keep them warm enough.
If you want to breed them in the future, first you need to find out if the other bird is a male. You also need to understand that if you set them up to breed, they will no longer be tame pets that you can handle. Both birds should be at least 2 years old. If she is younger than that, she really should not be with a male yet. She has to be on a nutritionally balanced diet and not a seed mix. She also needs fresh foods. They need a nest box and a private place for mating and caring for the eggs and chicks.
If she is a pet and you want to keep her that way, I would recommend discouraging egg laying by making some changes. You need to do all of these things to discourage more egg laying. Keep in mind that to lay eggs, she needs longer daylight, warmer weather, abundant food, and a quiet, private environment. Your goal is to reverse these conditions.
Limit her light to 8-10 hours by covering the cage early each evening
Do not give her anything to use as a nest – no bird huts or tents, no box, bowl, etc. If she decides to sit in a food bowl, remove it and replace with smaller cups.
Do not give her anything to shred such as paper or cardboard.
Rearrange the toys in the cage frequently.
Move the cage to a different place in the room. Move the cage about once a week, or whenever she shows signs of nesting – settling on the cage floor for example.
If she is let out of the cage, do not let her get in any dark cozy places and don’t give her free roam.
When you handle her, limit any petting to her head and neck – do not pet her on the body.
If there is no metal floor grate, then do not use any bedding or paper in the cage tray – leave it bare and clean it daily.
If she continues to lay eggs anyway, then you may have to take her to an Avian Vet for a hormone implant or shot. The implant seems to be more effective and lasts longer. But most of the time keeping her environment changed around works well.
Thank you for asking Lafeber,
Brenda