Hi M.--I have little girl that sounds very similar. She is 2 now and loves books so much that she picks out two to sleep with every night. But at one, she would hand me another book as soon as I started reading the first and hardly looked at the pictures. She would often try to turn the pages faster than I could read or walk away from me while I was reading the book she picked out...this lasted about 5-6 months, but I kept reading to her anyway (I'd read as she played near me or just read what I could get through before she lost interest). I also tried to teach her that books aren't the same as other toys--we can't throw them, rip them or step on them.
I'm also a speech-language pathologist, so I know a little bit about literacy and pre-literacy skills. So, my advice as a professional is: don't panic if your kid isn't paying attention to an entire book at 1 yr. Model "good book reading" behavior for her (look at the cover, turn the pages from left to right, label and point at the pictures, etc.) and consider any attention she pays to pictures positive. Think of labeling and attention to pictures as pre-literacy skills; these skills a crucial to speech and language development too, so as her language skills and vocabulary increase, she will have more interest in books.