I have a chihuahua mutt, Malchi, he is skinny, you can feel his ribs and spine.
But it has more to do with him being high strung, I swear he can hear the ladybug walk on the lawn across the street! He does get cold easy, so you might want to think about a winter coat or too. Too much weight on the little dogs is really hard on them too. Since you have no records, you might want to have her get a new rabies shot since it is the law in CA that all dogs have them.
Your vet might skip the other vaccines because she is older
And thank you for picking her up! Pit Bulls and Chihuahuas fill the pounds and an older lady with a bad leg might have never been put up for adoption. And might be why the old owners abandoned her.