How long was Big Red married?

Since Big Red is a dog, and since the story and its characters are grounded in realism, you must be talking about Big Red's companion who Danny finds to mate with him. Her name is Sheilah Macguire, and she first appears on page 177 when Danny picks her up from the train station. Like Big Red, she is an Irish Setter.
At first it doesn't quite work as Danny had hoped. Far from being attracted to Sheilah, Big Red is jealous of the attention that Danny is giving her. As Ross states:

He's been king-pin 'round here long's he's been here. Now you've got another dog to pet.

However, a few months later, Sheilah is pregnant. She gives birth to her litter at the end of the book, on 217, during spring. Danny collected Sheilah in late Febuary, so at this point Big Red has known her for around two or three months.