All tents that use trekking poles are available with poles for minimal extra $ and maybe 2 extra ounces. The "cottage" manufacturers all sell poles for their tents, or you can get the stouter ones from Ruta Locura.
Check out tarptent.com, sixmoondesigns.com, lightheartgear.com, zpacks.com, mountainlaureldesigns.com
For you and the dog, you might want something like a "1 1/2 person" or "1+ person" tent. I have crammed myself and my dog (a bigger than yours) into a solo tent (Six Moon Designs Lunar Solo), but it was extremely cramped during the week it rained every day from 2 pm until dark, forcing us to spend evenings in the tent! The two of us also kind of overwhelmed the ventilation system.