Well I can't tell you what to do. But I can share my experience.
My cat is a he devil and I love him. He is indoor/outdoor and that is kinda stressful because I worry about him. But he's older now so really he just goes out, does his business, then comes back in. He will probably be my last kitty tho. They can be a bit of a pain....scratching furniture etc.
My dog is my true best friend. I love him so much....boundless joy from that guy. He is easy too....but requires lots of love and daily long walks. Oh and don't forget the cost of animals....that's a thing if you want to truly take care of them.
I guess what I'm saying is yes. My animals definitely help me with sadness and anxiety. Nothing is cuter than saying good night to my furbabies, one at my feet and one by my side. My dog loves me, is always happy to see me and teaches me what pure gratitude looks like.
You decide when/if you're ready. But joy is what animals provide. And with joy and love in return? Well its a win win.