Material for shade tarp?

80% sun block gardening cloth

I think something metallized would provide the most protection from the sun's heat. A space blanket would work well in calm air, and metallized ripstop nylon would work in windy conditions.

Harbor Freight has screen cloth. Inexpensive and lightweight. I bought 2 rolls last year and was able to feel the weight and texture of it. I approve :-) Your dog will also. One roll will last a long time.

http://www.harborfreight.com/double-garage-door-screen-68310.html

Sells a 10 buck "backpackers tarp. Urethane coated, 5×7, 8.1 oz., 10 bucks.

+1 on garden cloth, it is very light. Another option could by noseeum or some kind of netting unless it needs to be waterproof.

I say use one of the original type "Space" blankets. Used as a sunshade with the silver side up, it blocks 100% of the light and probably 90% of the sun's heat.

Description of the Grabber brand blanket: "Made from superior insulated Astrolar Fabric, Plastic Film and Pure Aluminum. Both waterproof and windproof. Features grommets in all corners for stability. Available in 4 colors. 5 ft. x 7 ft., 12 oz. in weight."

Not a lightweight backpacking item, but perfect for your use.

A poncho with tie-outs works great. Makes a good rest stop and cook shelter too. And by golly, you can wear it for rain gear :)

On the bargain side, the cheapest blue poly tarps tend to be the lightest and you can get green or brown ones too. I've seen small ones on sale for $3-$4.

Depending on the dog, an umbrella might do the trick and setup time is about as good as it gets.