Q- Is the Government's proposed 'No Jab, No Pay' policy legal?... This policy takes away a parent's ability to receive childcare/welfare payments if registered as a conscientious objector--that is, to have official endorsement from a medical practitioner who is satisfied that the parent's decision is well informed.

Vaccination is a medical treatment, hence requires parental consent....   This looks like financial coercion to me, especially in consideration of the legal definitions of informed consent and duress. Further, the Federal Health Department recognises that for consent to be legally valid it “must be given voluntarily in the absence of undue pressure, coercion or manipulation” [Australian Immunisation Handbook, pg 26].- Hannah

In short, the answer to your question is, yes it is.  

The long answer requires following a chain all the way from the Constitution of Australia to today. 

The Commonwealth has the power to tax as granted by S51(ii) of the Constitution. The Commonwealth has the powers to enact laws regarding:

...taxation, but so not as to discriminate between States or parts of states.
— Section 51(ii) Australian Constitution

Because of the way our Constitution requires taxation laws to be implemented, there are a variety of laws that deal with specific taxes, as well as how those taxes are meant to be implemented.  You won't find them in one single place, that's a safeguard in our Constitution that really doesn't concern us right now so I'll leave it at that.

In the year 2000 we got a brand new taxation system, the GST or the Goods and Services Tax. As mentioned above, we don't have one single tax act we have several and one of them is the A New Tax System (Family Assistance Act ) 1999 (Cth).

The Family Assistance Act established the types of payments families with children could and would receive from the newly raised tax revenue to help them raise their kids.  The Act provides criteria for eligibility for the payments and in some instances allows the minister of the day alone to make decisions like what the immunisation schedule for Australian children will be and so on.

The decisions are referred to the minister to make because its easier this way.   This type of decision making is called deferred legislation and if it were not available every time new scientific research indicates the immunisation schedule should change, or if new vaccines are available the Act would have to be re-written, re introduced to Parliament and then reenacted- just for one small change.  This is common practice across all areas of legislation and in all aspects of law.  Ultimately, the minister is accountable to parliament for her decision and then ultimately to you, the voters.

What the Government is planning to do is to change the eligibility of people who access family benefits from its taxation revenue.  The minister or the government are not making anyone vaccinate their children, they are merely changing the availability of payments, so that anyone who has not vaccinated their children will no longer be eligible to draw down payments from the consolidated revenue.

It's both a 'carrot and a stick' approach.  If you vaccinate your children, you get family assistance to raise them, if you do not vaccinate your children then you don't get commonwealth money.  They are not forcing the vaccination of children, but rather rewarding the vaccination of children. People can still choose to object to vaccination, but they will not receive commonwealth money.  

It's as simple as that. Just to be super clear, the government is not forcing the vaccination of children, it is rewarding those that do.  Can the government force people to undergo certain healthcare procedures against their consent? Well, yes, but that's usually reserved for very serious diseases.  If you had ebola and insisted on going to the shopping centre you'll find out very quickly that you can be detained and forced to undergo treatment, or at least be quarantined.

You could make an argument that this law and change of policy is discriminatory, which strictly speaking it is.  It is granting access to benefits to one group of people over another, however the Commonwealth argument that this is good public policy for the majority will win out.

Reams and reams of scientific papers completely debunk any myths about vaccination causing significant side effects either due to the preservatives in vaccines or the vaccines itself.  In fact, there is more cyanide in an apple than in a vaccine.  

Vaccination is really, I think, one of the greatest achievements of humankind.  Putting some men on the moon is surely an impressive feat for the men who went there, eradicating diseases like smallpox and polio from the face of the earth? That's just genius.