As everyone has told you (more or less) it is different for each person, and I think, different for each pet. I am usually a multi-pet household, but I have found when I was without any, I adopted new ones much sooner. One of the reasons I choose to have multiples, but that is just what works for me. I lost Sugar, my first greyhound, in July. I am not 100% sure I am ready for another, but Fletcher, my other grey needs another dog, so I started looking. I saw quite a few that looked nice, but... Then I saw Molly's (aka Momma) picture, and knew she was the one. She's coming home tomorrow, and I feel that it is right.
So, my long winded advice , start looking, when the right dog finds you, you'll know. It may take a few weeks, a few months, a year, whatever is right for you and your family.