Include side on silhouette of pets-dogs, cats, birds (different sizes)-timeless and endearing as association important without distraction re breed and look.
Include tree ideally with roots below ground as per image (attached) and rainbow touching it or linked- this gives rise to using this elements to determine shape.
Can add paw prints around the lower part or either side.
The brand could be embedded or reversed out of the rainbow.
The logo should be enclosed so it can be transferred to a memorial plaque/card.
Needs stature and distinctiveness, yet has elements of playfulness and freshness as a trademark.
Colour is important (as wish to associate with primary colours and rainbow with silhouette style gives plenty of license and distinctive recall.
Also depth of field-3D impression is important or somewhat dynamic-motion is an option as well.
Must have international appeal
The tree, roots and pet association are vital.
The brand name should be embedded within the logo shape.