
Eddie if you married yoiur first cousin you would both have 2 Grandparents in common. So your childrens pedigree would show the same Great Grandfather in the third generation (as in this dogs pedigree) and also the same for one of the Great Grandmother appearing twice.
Now such a breeding would be perfectly acceptable in human society, where the main restriction isn't sue to health but morals, which so not apply to animals.
So my answer would be no this is not an iresponsible or overly close mating, sounds like second cousins had been mated.