I just love Brugmansias, but I can't buy one because I'd be too
worried about my dog who has a habit of sleeping under trees. Is there
a similar looking non-poisonous plant/ornamental tree that can survive
in zone 8? Any information would be greatly appreciated.

First, a Brug may survive zone 8, but unless you either bring it inside or
under cover in winter, it will be severely cut back. They really work best when
put in the basement and watered but little until Spring.

Second, they aren't trees, and I can't imagine the dog sleeping under it, or
suffering even if he did.

Third, no, there isn't any other equivalent.

What makes you worry about the dog?