Hi there......
I am not familiar with Eclectus birds, however found an interesting link pertaining to the peeling of beaks, their diets etc.
Hopefully other members will share their knowledge with you.
A birds beak is like our fingernails. I will at times slough. If it is excessive then a vet visit is needed to rule out vitamin deficiency and possible adjustment to the diet.
Mine is about 7 months too and it peels a little. I haven't put much thought to it. Just thought it's part of their growing up. Willie's beak is going to loose the black and turn bright orange in a couple months, I would think its just part of the process. But then again, I could be wrong.