Alchemy is the deconstruction and reconstruction of matter.
With this you could turn a book into a tree, a bomb into smelly odors, and living things into other living things. The only problem with the third is to deconstruct something to make another, you must deconstruct whatever you are changing completely. In other words you would die and something else would take your place. That's what happened in the beginning of the cerise, when Ed and Al tried to bring back their mother. There was no flaw to their calculations, yet still they brought something else to life, not their mother.
If you were to transform yourself into a furry with alchemy, you would have to safely remove your soul and brain. From there you can do what ever you want to your body, and once it's done you would place it back into your new body. Yet of coarse, you might as well create a second body and transfer immediately after being removed from you original body.
Also you have the problem where the new body might see you as a threat and try to remove you from its body. Wrath was the twelfth contestant to become a homunculus. All the others died.
Personally I wouldn't try turning myself into a Chimera either. The chances of surviving the transformation was one out of thirty six. only a handful of chimeras were successfully able to become what you would call a chimera. All the others became a waist of space and were tested for other military experiments.
Just watched FMA brother hood this morning, and I have read the full manga. Big fan of that kinda dark heroic story.
Also with genetic science, the human race can now manipulate the genetic code. Give us around a 100 years and we will be mutating our species so we can survive space travel, and become a more powerful race. That's if we don't do anything stupid in the process. In the end, I would rather wait for that technology to be completed than trying to use alchemy. Genetics is true science, alchemy is... not so much.