Hi, Yes, that is very doable. Ideally you'd want to build a simple jig, like this one:
This jig makes it easy to make any dado or groove. What makes it so great is that you fit a shelf or other part that will go into the dado, then snug the movable part against it. Then with a plunge base, you push a bit with a bearing down into the jig's opening and by making two passes, you get a groove just right for the part that fits into it. You could also do this with two very straight boards, clamping one where the top of the groove goes, fitting the piece and snugging the other board up, then clamping the second piece down.
You plunge the bit down about half the thickness of your workpiece. Your router has a quarter inch collet, which is pretty light for dados, but it will work if you don't rush it or try to take the full depth in one or two passes. There are several bits that will work for you, but I suggest you use one that gives you a flat bottom. Here is a picture of a mortising bit. I'd use a 3/8ths cutter with that router.
What you want is called a stopped dado. You plunge the router in at the starting point of the dado, and lift it when the bit hits the other end. You make several passes (the picture is a 1/2 inch shank, and will handle the lateral forces better than the 1/4 inch shank).
This gives you a nice flat bottom (better for glue), but the ends are rounded off. You square the ends up with a chisel (half inch size for 3/4 inch dado). Sharpness counts, and one investment that pays off is to buy a set of really good chisels, and read up on the work sharp method of sharpening them with sandpaper. You want to lightly cut the surface you want to trim square so it doesn't splinter on you, especially with plywood. Slowly and carefully shave the ends square, you can lightly tap with a hammer or mallot, but your own weight is enough. Make sure bottom you trim out is flat.
This sounds more complicated than it is. If you don't have a plunge base for your router, I suggest you get one. Most trim and medium duty routers have them available.
When I was learning woodworking, I had more money that time, so rather than build a dado jig, I probably would have bought one. Rockler makes an interesting one that uses a particular straight edge.
The jig is about $60. It requires a specific straight edge guide that isn't included. Just be sure the base will work with your router. Rockler Perfect Fit Dado Jig
. It even has dust collection.