Can I switch the nest of my Lovebirds?

I adopted two Lovebirds and they had a clutch of 5 eggs, I didn't time the hatching of the eggs properly and they hatched a week before I was prepared. At this time 2 eggs hatched (starting on the 8th) unfortunately the eggs and young are in a plush toy instead of a proper nesting box. My question is can I move the eggs and young into a new nesting box or is it a bad idea? The nest they are in now is really unsanitary and small and I really need to move them. Does anyone have a suggestion?