My chinchilla, Willow, and my dog, Toby, insist on seeing each other. They both get depressed if I don't allow them near each other.
Before anyone begins to lecture me, I know that chins can trigger a prey response, but if you met my Toby, you'd see in an instant there's no chance of that.
Toby is a big baby and scared of everything. Literally. He barked at a butterfly, and then barked at his echo. He has no prey drive at all, and if Willow gets too close, he crawls backwards out of fear.
The only thing in danger of Toby, is your face when your laying down and he wants petted. He loves 'sneak-attack' kisses.
If I believed that the safety of any of my babies (pets) were compromised, I would not allow them to be in the same room.