You need to be very careful about allowing them to interact due to the differences in size, and particularly beak size and strength. Right now, the budgie might be more of a danger to the conure, because she is mature and adept at using her beak. The conure is young and will possibly be unsteady and timid with her. Your budgie is going to be very jealous and you need to be careful about interacting with the conure around her. A territorial female budgie can be unbelievably vicious. She can easily pin down a baby conure and inflict serious damage. A budgie will step on a rival’s neck and proceed to ravage the bird’s head. This can happen fast and be serious or even deadly at the blink of an eye. However, as the conure grows and gains confidence, she is capable of injuring or killing the budgie. These birds do not come from the same continent in the wild, so they are not intended to interact. I definitely would never cage them together. You may see cases of “odd couple” birds that are companions, but generally these are birds that are raised together. And sadly when the beak size is very different, the larger bird will sometimes hurt the smaller bird without meaning to. So let these gals enjoy living in the same house, talking to each other from their cages, but generally not having contact.
Thank you for asking Lafeber,