Yes, single female parrots will lay eggs. It is likely that the eggs she has laid this time are normal size and she laid under-sized eggs before. You should leave the eggs with her if she is sitting on them so that she will hopefully finish this breeding cycle and not lay again anytime soon. She will likely push them away in a few weeks if she has not broken them or eaten them in the meantime.
Chronic egg laying is a real concern, so you may have to make some changes if she continues to lay eggs after these are gone. Laying once or twice a year is fine if she is on a nutritious diet. But laying year round is not good for her at all. Things that can trigger egg laying are nutrition, environment and handling. Try not to over pet her – this means stick to head scratches and don’t pet her on the body – especially the chest, lower back or around the base of her tail. Warm weather or keeping the house warmer during winter can trigger egg laying. Also feeding a lot of fresh foods can contribute because they nest when food is abundant in the wild. Longer exposure to light is also a factor, so cover her cage in the early evening to limit her light exposure and keep it covered all night.
Thank you for asking Lafeber,