I've just read an interesting article that I think
would make for a robust discussion. The link
below explains further:

http://torrens.edu.au/blog/what-degrees-ministers-australia-have-and-why-it-matters#.YWJQw9pByUk

Quoting from the link:

" If you're employing a tax agent to sort out your
finances you want to know they've studied accounting.
So what about the group of people we've "hired" to
run the country?"

"Some ministers are incredibly competent. However
it's not uncommon in our political system for
politicians to be handed a job in an area they've never
had any experience in. That's not great for obvious
reasons."

"Take Sussan Ley for example. At the moment when the effects
of climate change are devastating Australia - she is our
Environment Minister. Has she studied biology,
environmental science, or natural resource management? Nope.
She has a Master's Degree in Taxation and accountancy.
And she changed her name from Susan to Sussan due to a
belief in numerology."

When it comes to being a Minister in the Australian
Parliament surely qualifications and or experience - do
matter?

what often matters is intellect and a desire to do the right thing.

What does being an expert mean beyond science and mechanical expertise where no doubt you need experience and qualified expertise, although not always.

Law and economics are less important.

Most economists are merely trained the same way, and follow the same tune?

Only a minority of people predicted GFC, including one female historian.

and most professors i knew knew were not that smart imo, although I am sure some would glorify their titles.

So my answer is no.

They must most definitely have at least some previous engagement/exposure to in the field they're engaged to represent.
Even more important than a Minister's degree of competence is that of the policy makers/advisors.

Just read that list, what a shock ! None of them had any exposure to everyday life before becoming ministers ! No wonder things are so wobbly !

Because Ministers oversee the administration of
their departments and are accountable to Parliament
for their department's actions - legal
knowledge would be an advantage due to knowledge of
government regulations and court procedures.

The advantage of having studied the law would give a
person analytical thinking skills, and the ability
to think clearly using logic and reasoning and being
able to be thorough and pay attention to detail.

Therefore -qualifications in law and economics would be
an asset no matter what portfolio one was given. It would also
presumably result in - a person having
excellent verbal communication skills and active
listening skills - which would be an asset in any
position.

anyone can learn fundamentals of law and economics Foxy, not that hard.

I represented myself against a QC and several lawyers.

Load of rubbish a minister needs a law or economics degree.