According to the Oregon Vetrinary Medical Association a 13 year old Cat in Iowa and a Ferret in Oregon both tested positive for H1N1 in the past moth. Both animals survived.
My understanding is that it is possible that H1N1 could crossover to other animals including dogs. However, for dogs the bigger concern is H3N8 (Canine Flu). Most dogs survive H3N8, although some dogs can get pneumonia which can be fatal if not treated.