Yes, so they do! On the subjects of death, burial, and the merits of human behavior vs. that of other creatures, you're probably familiar with these lines from Byron about our relative regard for men and dogs in death:
"When some proud son of man returns to earth,
Unknown to glory, but upheld by birth,
The sculptor's art exhaust the pomp of woe,
And storied urns record who rests below;
When all is done, upon the tomb is seen,
Not what he was, but what he should have been:
But the poor dog, in life the firmest friend,
The first to welcome, the first to defend,
Whose honest heart is still his master's own,
Who labors, fights, breathes for him alone,
Unhonor'd falls, unnoticed all his worth,
Denied in Heaven the soul he held on earth:
While man, vain insect! hopes to be forgiven,
And claims himself a sole exclusive Heaven."
(I apologize if this small observation is slightly off-topic.)