Is Dalton's Atomic Theory a theory or a postulate?
It is most definitely a theory. The 4 points you mention could be construed as hypothesis by themselves. But Dalton went further, he put them to the test.
The results of his exeriments formed yet another component of his atomic theory called the Law of Multiple Proportions. This law served as proof that the other components of his theory were true. I used to spend most of a class period explaining this law to students, it's best you search the web for a complete explaination but I'l give you a brief summary via example.

Say an experiment shows it takes exactly 16 g of oxygen to combine with 12 g of carbon to make carbon monoxide. Now suppose we make carbon dioxide. We would find that it now takes 32 g of oxygen to combine with that same amount, 12 g, of carbon. So, for a fixed amount of carbon, the amount of oxygen required to make the two different compounds can be expressed as a small, whole number ratio. What would explain this better than to surmise that elements come as particles and thes particles combine in small, whole number ratios to form compounds.

When a hypothesis have been proven by repeatable experimentation, we call it a theory.