Unplanned Baby - Need Help Please

[Jez 0]

Hi All, I am completely ignorant on baby budgies and need some advice.  
 

To cut a long story short, I have a female budgie who laid two eggs in the bottom of the cage, on the plastic tray under the grate (which she has gnawed through).   She has been sitting on these eggs on the hard plastic tray for weeks.   Given their is no nest or soft material I thought the eggs would be dead.   So it was a surprise today when one hatched.
 

The plastic tray  does not seem a good place to me to raise a child.   Could you guys please advise me whether I should add a nesting box or nest of some sorts and move the baby into it - or will this upset the mother too much?