I think the contest would be fun if it don't get too complicated.
I would not have the 'cutest' dog, cat, pet as that could hurt feelings. I think something like funniest would be fun and not hurt feelings.
Myself I would keep it to just funniest dog, funniest cat and funniest pet. The three catagories that are here in PetTalk.
No writing contest, to me it just complicates the idea, it should be fun for everyone whether they participate or not.
Simplicity is the key, you will get surprised how complicated it can get with this many people who may participate and those who may join to get into the contest.
Just my ideas
Jackie