Very very difficult! This is a mismatch. There is very little in common between these two. Goat and dog are unsuited for each other as dog has a strong personality and goat is hard to deal with in the long term, which leads to lots of misunderstanding and frustration. Goat will just leave. (Source: geomancy.net)
Goat Man & Dog Woman
It is not possible for them to have a happy marriage. Both of them are too pessimistic and do not hold any hope for anything. There will often be disasters.
Dog Man & Goat Woman
There will not be happiness. It is hard to tell which one of them will get nervous first. Both of them will make the other nervous. There will be one disaster after another.
(Source: Love & Luck in the Year of the Dog)