I think it is normal . I felt this way when I got Cabo, since Tux was my first dog and was used to being an only dog, and used to it being just me and him. Then I got Cabo, and then I married my husband who has Cadbury. Tux adjusted just fine. I try to do individual things with each dog, Cabo is doing agility and Tux is doing barn hunt right now. With only having one dog, it is still easy to take Koopa on outings and such where it is just you and him.
I am looking forward to pics of Koopa with your new parrot!