What title to put on a professional business card, for a person with a PhD
"Dr Name, PhD" is redundant, so this usage is often discouraged. If you are going to indicate the degree, I'd recommend "Name, PhD" rather than "Dr Name" since it's more informative (at the very least it will keep anyone from thinking you are a medical doctor). In the U.S. it's not common to indicate the university, but I think I've seen it more often in other countries.
I'd suggest thinking carefully before indicating your degree on a business card. Some people without PhDs may respond bitterly, like you are bragging about your accomplishments or implying that your expertise is more valuable than theirs. At the same time, some people with PhDs will look down on it as well, in a status hierarchy:
Some insecure people without PhDs feel resentful and don't want to be distinguished from PhD holders.
Some insecure people with PhDs try hard not to be confused with group 1, thereby irritating those people all the more.
Some better-established PhD holders aren't worried about being confused with group 1, but now they don't want to be confused with group 2, so they pointedly denounce emphasizing your degree as being tacky and in poor taste.
As a rule of thumb, I would omit the degree from your business card unless it's important for your credibility (i.e., the skills from your PhD are professionally important and people would otherwise assume you don't have them).
The one situation in which you should absolutely not indicate a degree is if it's irrelevant. For example, if you're an accountant with a PhD in literature, then your business card should not read "Name, PhD."
My time in industry is longer than in academia. I would like to provide you with my opinion.
I would suggest
Name, PhD in Discipline name, University name
Job title
I think university name is optional. The discipline name is necessary because people want to know what you know. PhD in physics is very different from PhD in social science.
Please be aware of the possible negative effects of adding the PhD title.
There are quite a bit anti-academia attitude in industry. Some people dislike academics. They believe the academians know nothing but theory. They rather do business with non-academians. For me, I deeply respect academics. I believe a company can offer me good quality products if they have PhDs as some of their employees. So, I am more willing to do business with them. However, I think I am minority. Many industry people do not think that way.
If your employer is a consulting company, your title can be helpful. The PhD title can convince your clients you can offer them high value services. If your employeer is a constructing company, you might want to think twice before you update your business card.
In your case, I would suggest "Yes, put Javeer Baker, Ph.D" on your card. You could optionally put "in social science" on it if you'd like.
I cannot speak about the culture in Australia, but in the United States and Canada, it is appropriate to put your title (Ph.D) on your business card if the industry generally is supportive of or respects academics, or in which high degrees are not common. I might guess Australia's culture is similar.
Industries that would want to be proud to have a Ph.D on staff especially would be non-profit organizations, advocacy groups, research think-tanks, and consulting. As you said that your employer was an advocacy group, I believe that putting your degree on your business card is beneficial.
Industries in which you would NOT put your degree on your business card would probably be software high-tech (because no one cares) or in academia (not because no one cares, but basically any assistant professor and up basically has a Ph.D and therefore it's not impressive), or, as mentioned above, a construction management company or similar.
(As an aside, a whole bunch of people at a conference I was at rolled their eyes when they saw one of the authors wrote "name, Ph.D" on a paper.)