I got a dog about 6 months ago--it's the first time I've ever cared for an animal in my life. It's been a fulfilling and fun experience.
In Episode 10 of the Highly Sensitive Person Podcast, I talk about how HSPs can have deep connections to animals due to our empathy and ability to pick up on non-verbal signals.
Resources mentioned in the podcast: This post by Dr. Elaine Aron about what HSPs can get from animals.
Related Posts on HighlySensitivePerson.net:

Could I handle having a dog?
Follow-Up: My First Experience Taking Care of a Dog
Anger is an emotion, too (about getting angry at my dog)