Here's an article from the BBC about training dogs to parachute with members of the SAS - http://news.bbc.co.uk/1/hi/uk/7518560.stm
Training dogs to parachute with soldiers is not a new concept. In the United States, this was first done during World War II. The book "War Dogs" mentions one dog who parachuted in the European Theater along with US Airborne troops, which, as far as I know, was the only combat jump any dog had during WWII. The concept of parachuting with working dogs was later brought back in Vietnam and, more recently, in the UK. (Long before this current article.)
The dogs don't jump by themselves, they are attached in a special harness to their handler and jump with them. This is not any more dangerous for the dog than rappelling over the side of a building with his handler or being lifted to and from a helicopter using a sling, both of which are frequently done with military working dogs and, in some cases, even with police dogs.
There are NO news articles I have been able to find that actually said what the SAS is planning to use the dogs that are currently in training for. I certainly have not seen mention of them "being sent in with cameras attached to their heads." I would assume that these dogs would most likely be used as sentry dogs, tracking dogs, or detection dogs. The UK has, by the way, currently one of the best working dog, and particularly tracking dog, programs in the world.
It's a military working dog's primary task to detect danger - either by locating enemy ambushes or locating explosives - and has been since we have had dogs on the battlefield. There is nothing "wrong" or "cruel" about this - it's what these dogs are bred, and trained for.
I think, like many petitions, they are written by well-meaning people who have little understanding of what these dogs will be used for (or are basing their opinions on sensationalized articles) or how working dogs in the armed forces are used. This petition makes it sounds like hundreds of dogs will be dropped without soldiers nearby, and left to run around with cameras - as if the dogs would know where to go or what to look for without their handlers nearby.