I vaguely remember watching this around 2011. All I remember is a male character that was either a demon slayer or exorcist. I believe a little blonde girl went with him. They traveled all over to help people kill ghosts and demons.
The first thing that comes to mind for me is Blue Exorcist/Ao no Exorcist and apparently it first aired on Netflix in April of 2011. There is a blonde female companion named Shiemi Moriyama and she's around the same age as the two protagonists Rin and Yukio Okumura. I'm pretty sure that's the anime you're thinking of, it's still available on Netflix too and the manga is still ongoing. Another anime that came up when I googled "anime about an exorcist with a blonde female companion" was "Beyond the Boundary" but the anime for that didn't come out until 2013 and was never on Netflix. There is a blonde companion but the character is male not female.