Getting and administering euthanasia drugs without a doctor is illegal, even where physician-assisted suicide is legal.
This isn't specific to euthanasia but applies to all prescription drugs. As long as the law doesn't let people decide to take even minor mostly-harmless medications without a doctor's approval, it will certainly not make an exception for drugs designed to kill people. Changing these laws is far harder yet than changing the laws prohibiting suicide and (non-medical) assisted suicide in general.
There are lots of drugs people can take without doctor's approval. It's just ones with harmful side-effects that are a problem. Drugs for euthanasia are, for all intents and purposes, 100% effective with no side-effects.
Over at Scott Adams' Blog you can find a very fine example of using the 'Rationality Engine' to solve the social problem of assisted dying.