It's always good to have some type of security background when trying for the CISSP.
Remember, this is a graduate level certification. The Security+ is for entry level admins. What the CISSP shows is that you have been in the trenches and now you have some experience with Security management. When I first took the CISSP, I failed the exam because I hadn't gotten out of network administrator mode. And the test questions do test that. You have to look at the exam from a manager's point of view. I would suggest being in the field for a few years before taking the exam.