Thank you so much for explaining that. Screws sound the best way and glue is fine once it is dried and the odours dispersed. And I am sure you will have done it carefully so there is no exposed glue to nibble. I use non toxic wood glue in wood houses when sticking legs on. I think the exposed edges of chipboard are just around the top where not accessible - easy enough to just stick a strip of melamine over them - I think you can actually buy the strips.
Glad she has gained some weight