Is my new puppy too young to let out in the backyard without supervision?

Adopted a 3 month old chihuahua puppy from the pound a month ago so I guess she's 4 months old now. She LOVES going outdoors to run around and play with my older larger dogs. She will jump on them and literally take off mouthful of hair! But they love playing with her even though she plays rough. I think... show more Adopted a 3 month old chihuahua puppy from the pound a month ago so I guess she's 4 months old now. She LOVES going outdoors to run around and play with my older larger dogs. She will jump on them and literally take off mouthful of hair! But they love playing with her even though she plays rough. I think it's because she spend all her life in a cramped shelter.

But what worries me is that she'll put anything in her mouth like sticks, rocks, poop, dead mice, and anything that's on the ground. I am worried she might choke or get poisoned. Plus there are hawks and great horned owls here which would have no trouble snatching a 5 LB chihuahua.

So should I not allow her outside anymore?
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