
It is natural for puppies to be curious and to play predatory games, so any pet that is not robust enough to handle it's attentions is at risk.
A puppy should most certainly be somewhere safe 24/7, if not under direct supervison, then confined to a small safe area. Giving them full run of the house is most unwise and will hinder housetraining, and encourage distructive behaviour, as you won't see when she starts on anything.
I had a pet Budgie, and unfortunately it was eaten my my then 5 month old first homebred puppy. One of the children had released the cage bred bird, which flew at about 18 inches off the ground, and instinctively the pup jumped up and caught it. With all the ensuing panic with child screaming the pup run areound and suffocated the bird.
This same dog as an adult oft6en brings me unharmed fledglings, and even the mice that my Dads cat has tormented half to death. Now her mother would say wither of these as food, and none of the others have ever caught a bird, so unsure what they would do.
As another poster said the bird should be kept in it's cage/aviary out of reach of the puppy. shouldn't be too hard as Maltese aren't very big or strong dogs. A baby gate across the door would probably be sufficeinet to keep pup out of the room, so as it didn't frighten the bird.
Now under strict supervison the dog can be trained to leave the bird alone while you are there, but I would never take a chance leaving them alone together unsupervised and free.