TL;DR This is almost certainly true
The US department of Census reports in 2010 there were 35,218,000 households with "own children under 18 years" (This probably excludes some households with children, such as those being raised by someone other than the parents). This is out of a total number of households of 117,538,000.
Dog statistics are a little harder to get accurate, but The Humane Society says 39% of US households own at least one dog. That would give a number of dog-owning households at 45,839,000 - substantially more than the number of households with children. Other sources have similar figures.
It's probably worth mentioning that the number of households who have ever had children is more than the number who have children now.