Let's start by saying that Passover is absolute heaven for dogs ....Rabbi Hammerman states his belief that, in Dog, Pesach is known as the "Festival of the Crumbs". He goes on to discuss a ruling of Rabbi Joseph Soloveitchik (The Rav, z"l) regarding toothpaste, and how that ruling applies to eating Pesachdik in general.
It helps, says Rabbi Hammerman, that dogs are automatically considered Sephardim - they are permitted to eat kitniyot (legumes) during Pesach - although he does not provide the source for this statement.
As one who used to ... enable his pets to observe the laws of Pesach, Abq Jew takes heart that places like Evanger's make the whole enterprise somewhat less of an adventure.
Click here for more of Rabbi Hammerman's Pesach / dog advice.