How high?

I would say your best bet would be to put it on a two grid high stand, or just put a lid on it.

I should have been more clear, I meant the solid coroplast sides, like is 10" tall enough to keep them from climbing over? My grids are 1 1/2 " so she can easily poke her head and partially her shoulders through them. (dont ask how I know hehe)

10 inches should be more than enough.

ditto to rabbits.

Ah, my bad. Stupid mistake.

Yep, 10" is more than enough.