This response won't sound like telling him to follow his dreams. Maybe he should. But for me it would depend on whether this dream has been consistent or if it's part of some larger pattern of "the grass is always greener in any other job but the one I'm in now." Only you can answer that, we can't.
This is the line that jumped out at me, and it's not really to do with being a cop or not:
"He's also always tossing around new ideas for jobs and where to move, so I also feel like he's kinda wishywashy..."
So -- he has a pattern of always wanting a job other than the one he's got at that moment? Is that a fair assessment of what you're saying here? Is that other, dream job always a law enforcement job, or is law enforcement just his latest enthusiasm, and in the past there have been other dream jobs he's said were The One, but which were never The One I'm Doing Now?
If I were you, yes, I'd look more formally into what law enforcement really involves but at the same time I'd ask the bigger-picture question: Does he have a pattern of always thinking that whatever job he's currently in is just not THE job and there's some other job (possibly one that seems more exciting) always just over the horizon if only he could leave this current job; if only you, dear wife, would be willing to take the risk with him; if only he could get the money to do the training; if only.....Maybe he doesn't do this, and the law enforcement dream is a real and strong and consistent one. In that case, get a lot more solid information and both of you get to decide, together.
I think you're sensible to look ahead and wonder if, should he actually become a cop, he will find that in a few years it's not what he expected, it's a lot of training and paperwork, and...there's this other career that would be just perfect for him, if only....
Look at the big picture and the big pattern, if there is one. He might need some job counseling to show him that the grass isn't going to get greener if he takes a pay cut just as you are considering the huge expenses of adding a baby to your home. Or if you and he -- together, not just him -- decide to go for law enforcement, he's going to need job/financial counseling as well, to work out how you'll manage with the pay cut.
It is not "unsupportive" to be realistic. "Unsupportive" sounds a lot like it's coming from someone who expects you to support him even if his thinking is based on emotion and not on what is best for you and your future kids. Job counseling could help him see if law enforcement is realistic. Couples counseling could help if this is becoming a real sticking point between you. It sounds as if maybe you and he approach life from quite different perspectives, which can work just great in a marriage--or not. If you and he have "argued about this for ages" already, imagine what things will be like when you have a child: Will he want to change again if this doesn't turn out as he expected? How does that help you pay for a kid's expenses and save for college? And so on.