The advertised deliverables were: project management of operations center, project delivery and contract management to name a few. Will these not translate into other sectors, say if i were to move into mining or oil and gas?
As a graduate engineer, the GOV job starts at ~$67k, similar to the private sector job. Both offer at least the mandatory minimum of 9% superannuation for retirement fund.
Although I have an MSEE in computer design, I never worked in the field. Instead, I made my living in project management and, yes, it works across all sectors. In public service there are probably more rules related to fair competition and you wind up having to give a contract to a contractor you would rather avoid, and you wouldn't even have on the list were it private sector work, but you have to go with the flow in the public sector.
My project management work was in the design and construction of high tech facilities (wafer fab, computer rooms, manufacturing facilities, that kind of thing) and it kept me fed all my life. My pre-grad background was Journeyman Electrician and this was a great place to start since every project is heavily into electrical systems. In some cases, the electrical system was the project.
So, after you get your MSEE, stick around for another year and get your MBA. You're going to be in management, not so much in engineering and an MBA will look good on the wall. You will already have all the technical skills required to enter the MBA program and it will be simple compared to BSEE. I didn't do the program but I was always fascinated by the sub-field known as "Operations Research" because I was interested in the computer solution to problems involving scheduling with constrained resources. I was really a code weenie at heart.
Get your public service employer to pay all costs of all education. The Veteran's Administration (VA) paid my way through under-grad and my employer paid my way through grad school. I suspect they would have paid my way through B school if I had asked.