Duke, who shared this personal snapshot of her brood with PEOPLE Pets, has opened her home to numerous cats and dogs over the years. When she juggled the responsibility of raising four small children in the '90s, caring for lots of pets were out of the question. But in recent years, as she began dating Reitman, animals have found a place back in her life – and she couldn't be happier! "Once I got with Joe, we started really supporting no kill shelters," she says. "I think that rescue animals are really amazing. There are so many animals that don't have homes. So if you're planning to bring an animal into your life, bring an animal in that needs a home."
Caring for their five rescue dogs is a responsibility everyone in the family shares, including Duke's children (Maud, 14, Leo, 11, Lucy, 8, Nelly, 7) with ex-husband Ben Duke. "They're responsible for feeding them in the morning and feeding them at night," she says. "Nelly is the only one who doesn't have a dog job yet."
Does she have any plans to expand her furry family? "We're not going to add to our brood of five right now," she says with a laugh. "But I want to get some sort of bulldog." For Duke, mutts are the only way to go: "Mutts are hilarious. I think that the funniest looking and best-looking dogs are mutts."
Watch Annie Duke compete for her charity Refugees International on The Celebrity Apprentice, which airs Sundays at 9 p.m. ET.