This is your petition, correct?
You have to have a plan of action, a solution before you can make such drastic changes.
You can't just make the change, and hope someone will come up with a solution after the fact!
Not practical and not going to work out well!
I do like a few of the ideas you have within such as an animal abuse database and making animal abuse legally more serious crimes thus with greater consequences.
However, there are already laws regarding breeder licensing. So I kinda see that as a bit of a waste of time (and money should it actually be discussed/considered by the house and senate). Really though, I fail to see how licensing is going to stop the euthanasia of dogs and cats anyway? It hasn't made much if any difference to date...
And sadly I also do not see banning the euthanasia of all healthy animals in shelters as feasible at this point in time...
I do believe that we have more of an owner retention problem than over population but simply banning euthansia will do nothing to resolve the problem. Education and shelters making improvements (systems to help make better matches, programs/staff dedicated to helping with training issues, better advertisement, etc.) can make a huge difference! And really that's where the solution to this problem is going to lie.
Furthermore I have an issue with the actual idea of banning the euthanasia of ALL HEALTHY animals. Sounds nice in theory! Would be fantastic if it would actually be possible. However, one really needs to also take into account dogs with behavior problems that make them unadoptable. What would we do with them?

Perhaps it would be better to focus on the way animals are euthanized! Fighting against certain methods of euthanasia would IMO be a more practical fight at this point.