I feel your pain Olivetree. I too had a little 12 month old (& her sibling, who is almost 4) who both started with me 6 weeks ago. For the first 2 weeks I felt like I needed 6 eyes to keep watch on her...and 6 arms to keep redirecting her. Now, a firm "No Sophia" works pretty well but she's also improved a lot in knowing her boundaries.
Re: "Also how the heck do I get her to sit for one song or one book! She's all over the place!"... You really got me thinking...I currently just let both of the 1 year-olds just play and wander during circle time...they do wander in for parts. I do make time for 1 on 1 learning with them at other times of the day so I don't worry about it.