It's correct! But you can also shorten it: " we went for a walk after dinner".

If you are confused by the fact that some people are saying it is correct, while others want you to add "had," It is because many native English speakers don't get instruction in correct grammar usage at school anymore. In the U.S., where I am, most people use incorrect sentence construction, and most would not know the term "past perfect" unless they are very interested in language or went to a very rigorous school. It is correct to write, "We went out for a walk after we had had our dinner," although this is definitely changing when people are talking informally. In another 50 years, this rule will probably be forgotten. :(

Really after 'had' you need another verb. This is past perfect emphasing diiner was over when you went for a walk. Had had Had eaten Had finished Are all possible. Finished is probably best. If you put it in the other order it is more a series of events. We had dinner then we went for a walk.

Nope, this is perfect.

All good.