yeah is me..again.. ;D ;)..you don't have to bother about filling them in. You have done good basic preparation and there is already enough depth to grow most of the veg..but when you plant something, put some multipurpose compost on surface and lightly fork it in into top few inches..that is the stuff that the new plant roots will 'grip' into..the fine stuff..until rest of the soil settles..and as time goes by and you or the daughter keeps mulching the bed the level will eventually start rising..that that's what you boards are for to hold it all in.
So for now what you've done should be plenty and even during this summer she could do a bit of 'lasagna' with her beds..keep piling some good stuff as mulch..little and often.. ;D ;)
