Is my cat still teething or just extremely playful?

My cat, Meeko, is 8 months old and LOVES to bite stuff. She'll bite anything. Furniture, people, toys, etc.. and she's always hyper. But, when she bites, she doesn't bite hard enough to draw blood, it's just more like a pinch. I'm just curious to as if she's still teething or if she's just being extremely playful. Also, Meeko was just recently spayed and had her first rabies shot on June 15th and was kept over night (it's policy), does that tie into it? Do you think I should get her some big toys like those big scratching posts with all the little holes in them (since she enjoys high places)? Suggestions?