The Dink Network

Obviously the gender of Ethel is up to her creator, Seth. He has made it very clear through Dink and his Mother that he considers her a female ("She's old, isn't she?" "Yes, Dink, she is.")

So I would say that there is no question about her gender, but only about what the picture is trying to mean. Given that Seth wanted her to be female, I find it very unlikely that she would have a beard.