Since I am also in AZ and seemingly have nothing better to do for the moment I'm going to weigh in here as well.
What I carry really depends on the where and what I am doing at the moment. For urban carry, I've always got a Sig 365 at 4o'clock
But, once I leave the concrete jungle for the cacti and mesquite, I tend to carry a .22lr revolver (Heritage RR 6.5" shooting CCI Stingers) for snake, small game and the very odd chance at a close coyote. This also doubles for many gun hunts regardless of if I've got the shotgun for quail/dove or a rifle for deer. I like having a small bore option handy.
When the mood strikes me and I want more oomph, I carry a Judge magnum, with the first 2 slots holding 3" #6 shot loads and followed by .45LC in the following 3. I've got the one with the 6.5" barrel and have carried it (unsuccessfully) on HAM javelina jaunts. For being a large handgun, it really does carry well.
If I had to choose 1 gun in my collection that I would be comfortable carrying regardless of the situation? It'd be that P365, hands down. It's accurate and it'll handle anything you might need to ask of it in AZ, whether or not it's 4-legged, 2-legged or even 0-legged
I've been entertaining the notion of a new bigger bore handgun for trail carry with a pack or on the horses, and I think a 3" or 4" .357 DA revolver would be about ideal for any situations I can think of in AZ.
After re-reading your post
@mrjashu , I think my actual recommendation might be for a .22 Mag revolver, like a Heritage Rough Rider or a Ruger Single-six. For shooting rabbits and whatnot, maybe give that 4" .357 a thought as well and load it with .38s. You may be happy with the combo