Here is some welded wire options:
http://www.tractorsupply.com/tsc/search/welded wire
Around here we have coons, bears, and foxes. They would rip through chicken wire easily, so that is why we need welded wire. If you truly believe that nothing could rip through chicken wire, then go for it. A fenced in area and 2 dogs sounds pretty secure. But i would hate to see a predator get in and kill your birds. I have lost birds to predators and it really is discouraging. I would actually go further down into the ground if i were you, maybe more like 12". And curve it out, and put bricks on it to weigh it down. Rats and mice can dig and get in. They will eat your chickens feed and possibly nibble on them while they sleep.