I'm going to ask for a weekend off from work when I'm explicitly hired to work weekends
Is there some kind of problem with the job?
My dog needs to be taken care of.
It's ok if you want to take a weekend off as your pet needs to be taken care of. I hope you'll be able to make some time for your pet.
Keeping on top of my pet's health is important to me.
Which is you being a great pet owner. Asking for time off of work for this is totally fine. Whether your boss gives it to you is another matter.