Do you think I should date someone three years younger than I am?
I think that's fine, are you worried about the age difference?
People might think I'm inappropriate for dating a younger woman.
I think three years is not a large age difference and if she makes you happy, then you should go ahead and date her. As long as she's of legal age, there shouldn't be any issues.
I don't know, I think people might judge me in a negative way.
If you feel like you're being judged and you're nervous about it, it doesn't seem like you'll be very happy in this relationship. Take some time to think about it and see if this is the right person for you and if you'll be happy together.