Don't rush the dating thing, please. I understand being lonely but you're trying to fill a void right now and all a new woman will be is temporarily self-medicating the pain away. It will cause you more pain than the M has done if done at the wrong time and it could hurt her also.
You can be alone for a while and enjoy being single. I promise its not as bad as you think. You get to learn who you are and enjoy life in a way you never have before. Be a single adult and heal from this before you jump into something new.
Accept what is, let go of what was, and have faith in what will be