Britain's Luftwoofe: The Heroic Paradogs of World War II
http://www.spiegel.de/international/zeitgeist/the-parachuting-dogs-of-the-british-army-in-world-war-ii-a-939002.html

No one can say for sure who the first dog to parachute was. This undated photo (most likely from between 1920 and 1924) shows members of the Colorado Air National Guard with dog Jeff, wearing his parachute. After making several successful jumps, he was killed in August 1924, when his chute failed to open

The idea picked up steam in the years to follow. Here, a piece in Popular Science magazine from November 1935 discusses Soviet experiments with parachutes for dogs.
Brian was a tough paratrooper. He trained hard for his deployment with the British Army during . During his training, he learned how to identify minefields. Then, on the battlefield, he protected his comrades-in-arms -- though not all of them made it back. On D-Day, he parachuted under heavy anti-aircraft fire onto the Continent. He was there when the Allies liberated Normandy. A few months before the war's end, he parachuted into western Germany, from where he marched to the Baltic Sea.
Less than two years after the war, Brian was given an award to recognize his "conspicuous gallantry." But the bronze medal was not the only thing that distinguished this special soldier from the majority of his comrades: Brian, the tough paratrooper, was a dog, a young Alsatian-Collie mix.
During World War II, the 13th (Lancashire) Parachute Battalion started an adventurous experiment as it prepared for D-Day: enlisting dogs into their ranks. The so-called "paradogs" (short for "parachuting dogs"

were specifically trained to perform tasks such as locating mines, keeping watch and warning about enemies. As a side job, they also served as something of a mascot for the two-legged troops.
Finding Heroes among Orphans
Andrew Woolhouse, an amateur historian, surmises that the battalion first got the dog in early 1944 because Lance Cpl. Ken Bailey "had a veterinary background." Woolhouse researched the battalion for five years and gathered the writings of a number of battalion members from both before and after D-Day to help him write a battalion history, "13 - Lucky for Some: The History of the 13th (Lancashire) Parachute Battalion," published this year.