I have really bad allergies in the spring and I have lived in (Peoria, Phoenix, Tucson and Flagstaff) Arizona all my life. When everything blooms I go off, so I don't know why people say the dry weather = no allergies.
There is a definite lack of humidity in the Phoenix area.
I lived in Peoria, the majority of my life and people wave but now that I have lived in Flagstaff, they are much friendlier up here. The smaller the town the friendlier, I actually live in Mormon Lake which is a tiny town 30 minutes from Flagstaff and we know everyone in our town. Our neighbors share fresh eggs with us, etc.
Where I lived in Peoria, we have had scorpions, 1 rattlesnake, a bobcat, and some coyotes. Because your dogs are small, you need to keep an eye on them. Scorpions are easily dealt with but rattlesnakes you have to call someone out. Bobcats and coyotes will and have killed and eaten small dogs. (The ones we have seen have run off, human presence scares them.) You just have to be attentive. Also be aware of the heat. Your dogs need several bowls of water and shouldn't be left outside during the hottest parts of the day. They can and will die if not attended to. Make sure your animals are disciplined and listen to you. We stayed out of conflict with the bobcat because our dogs listened to us, came back inside and did not try to investigate the animal. Also there is a leash law in AZ.
Also as a pool man's daughter, if you get a pool, please make sure you look before you empty the skimmer, on the job we have encountered live rattlesnakes, general snakes, tarantulas and all kinds of critters alive and dead. By the way tarantulas are actually the least aggressive of many spiders so they won't attack you but could bite if you disturb them or try to grab them. Generally they try to avoid you. My dad has seen a mountain lion in a pool on the job, but they really don't like people and it ran off. As long as you haven't accidentally cornered them, you should be fine. You see more wildlife with pools because they come for the water.
You might need to inspect your yard if you have thick areas of plants. Avoid having piles of junk or wood where snakes like to hide to keep cool. Scorpions can be hard to see, I have never had a dog be stung by one but as long as you can get to a vet, it should be a minor experience. Unless you have allergies, scorpions stings can be minor (though they require professional treatment).
Be aware though that Africanized bees do live in AZ and they can kill a dog. They are an aggressive hybrid of European and African bees and when disturbed they will all attack. If you notice bees hives near or in your yard they need to be removed. (though they may not be Africanized bees)
Our German Shepherds have severe allergies to the weeds that grow in our yard we are very proactive about keeping them up.
Just remember that is is very warm in Arizona, you need to be aware that you need water on you at all times, including your car should it break down. Pay the money to have your AC checked out each winter because if it breaks down you'll be in a long line to get it fixed. Don't try to go through a wash in monsoon season when its flooded...your car will not make it. Get a vet close by and talk to them about what to do should your pet get bit or stung.
As for the wildlife just be smart, keep your ears and eyes open, when hiking it is best to make some noise, whistle, sing, talk...the wildlife want to avoid you. Watch where you step and put your hands ( I almost put my hand on a scorpion while reaching for the garage door opener without looking).
And Welcome to AZ, you'll really love it...if you like the heat.