There are many different kinds of learners: visual, auditory, and tactile/kinesthetic are the three basic ones. You probably have a tactile/kinesthetic learner which means she like to explore with all of her senses and engage in her environment rather than watch or listen. And, of course, this is developmentally appropriate to not want to sit still necessarily--you already had thought of this when you said that she is "really into discovery". That's exactly it. Allow her to engage in the book as she sees fit HOWEVER there are things you can try to help her become a lifelong reader (this is coming from experience as I have a 17-year-old and 10-year-old who are still avid readers and do very well in school--the 17-year-old is the kinesthetic one and the 10-year-old was the visual one who wanted us to read to him several hours a day at the age--he could sit still for hours!!). Here are some things you can try that I tried with my older one:
1--model reading in front of your child as much as possible
2--turn off the t.v. (We didn't allow them to watch t.v. until they were about 3 years old AND even now we only allow 1 hour a day--combined with computer and computer games--and we have no video games at all!)
3--try reading three very short books every night (as, hopefully, she will be tired and won't want to be as grabby) and gradually work up to longer books
4--when you read to her, allow her to pick out the books and bring them to you. Then allow her to play a game of some sort in order to pick which one to read next(or just pick them out). He always played "eeny meeny miny mo" moving his fingers across the books (nice for the tactile kids!).
5--select books that are age-appropriate for her (board books at this point), but that hopefully tell a story with a beginning, middle, and end.
6--Read the same books over and over so that she can read (or mumble) along with you--which will excite her to no end!
7--If you start to read and she grabs it away, you can tell her that she should read the book to you and that you can take turns. This way she is learning to share while she lets you read a little.
Try all or some of these and please let me know how it works out!