Depends on the size of the mesh on your dog crate. It needs to be 1/2 inch - the chicks will get out through 1". (And the rats can get in, too.)
We've lost baby chicks to rats, hedgehogs, magpies and the cockerel. Oh, and a calf, when an errant chick got under a gate and got trampled. So yes, best to only let them out under supervision for the first 4 or 5 days, at least. A coop with a run - like an ark - is the usual solution. Simple to make an oblong and cover in fine mesh?