going red

First let me say I am not a professional haircolorist - just so you know. Since you already colored it dark, remember that color won't lift color.  Just putting red dye on it will likely not do much of anything. If you want dark brown hair that has a dark reddish hue that you will likely only see out in the bright sunlight, that is likely what you will get just dyeing it red.  That can look nice, it depends on how bright or light of a red you want.

If you want redhead red, where its bright like natural redheads have, you will have to remove your color and possibly lighten it some after that (depending on what color it comes out after the color is removed), then dye it.  This could get complicated, remember to test strand everything if you choose to do this yourself.  

To remove your color you can try Colorfix- that you can get from a beauty supply shop and its not as damaging as bleach, so its a good thing to try first, but it doesn't always work on permanent black, so it may not do much.  If it works, and you wind up with orangy hair after your dye is removed, then you are probably good to go since you want red, but still test strand before dyeing it all.