I would try for a slightly larger pack, but you're headed in the right direction. Check out
GoLite packs and shelters.
There is a growing selection of tarps and tents that are ultra light. Henry Shires and Six Moon Designs make some of the best. I use a Six Moon Designs
Gatewood Cape, which provides me with a poncho/cape for rain gear and a 35 square foot floorless shelter at 11 ounces. It uses one pole and I use trekking poles which cover that, or you can buy a single carbon finer pole or cut one where you camp. It has enough room for your dog too. If bugs are a problem, you can get single-wall tents from the 2 suppliers above that are under 3 pounds.
There is a dedicated following of hammock users, but there's no real deal for your dog except sleeping under. Hammocks present their own set of problems in insulating the bottom side. You end up with a rig that is actually heavier.
Tarps are great shelters, although I don't have a good answer for the dog. Maybe a light aircraft cable lead?
There are flat tarps and catenary cut models. Catenary tarps are cut so they have a curved ridge line when pitched, which makes them more stable in the wind and any will have beaks to help extend protection from rain. Catenary tarps are more expensive and more limited in pitching options. Poncho shelters usually require a bivy bag to make up the lack of protection. An 8x10 or larger tarp will do the trick. You could experiment with a blue poly tarp and switch to silnylon if it suits you. Gossamer Gear, Integral Designs and GoLite make good tarps. For a simple flat tarp, Etowah makes less expensive models.
You will want a sleeping pad-- more to insulate you from the cold ground than soft comfort. Simple foam pads like the RidgeRest are light and will keep the ground from sucking the heat out of you.
offers some of the lightest, thinnest pads. Consider a small thin pad for your four footed buddy too.