Pet sitting prerequisites are pretty loose. Sitters (probably) have to enjoy interacting with animals, or their pet sitting careers (probably) won't work out well for them or the animals. It's also best if they don't have any serious pet allergies, as the constant fur and dander may give them more trouble than they bargained for.
Beyond those qualifiers, it's helpful if the would-be sitter had some previous positive interactions with the species they'll be visiting. They might be comfortable with dogs' wide-open, slobbery greetings, for example, but find that cats' unpredictable nature intimidates them.
In this case, it's perfectly acceptable to limit services to households with canine members. They shouldn't, however, be surprised if they don't get an invite to the D.C. National Feline Convention in September.
Of course, sitters can always prepare for their future careers by racking up some volunteer animal-handling time. Local animal shelters will probably welcome an extra set of hands to socialize with the facility's dogs and cats. The shelter staff might even allow volunteers to share in the pooper-scooper and litter box patrol. Now there's an added bonus.
Aspiring sitters should also consider logging some hours as a grooming shop bather. They won't make much, it'll involve wrestling with animals of all sizes and athletic abilities, and they'll smell like wet dog, but they'll likely become a more competent handler because of it. And if they can expand their expertise to grooming talk show hosts, some of them may even become qualified Chelsea handlers.