Sweetness with a Lot of Love & Logic

How can someone filled with so many sweet moments, be filled with words like "I bite" or whining, whining, whining? This is the point we are at. Claire is an awesome kid, really the best in my biased opinion, but she is whining WAY TOO MUCH. She whines when we put her down, when we leave the room, when we walk faster than her, when we put her in her high chair, when we tell her "no," and on and on it goes. This difficult behavior makes for some very challenging moments. The second behavior that I am less than thrilled about is her biting. She bites everything and anything--the couch, the table, the dog, me, Chris. You name, she'll bite it. Granted her bites are less than actual bites, but regardless, the intent is there. It started out of frustration--bumping her head on the coffee table resulted in a bite (it was the table's fault), but it has bloomed into something else. Now she actually bites, looks me right in the eye and says very matter of factly, "I bite." Ugh. How do you look at that sweet face and not laugh? So what is a new Momma to do? I ran to our local library and checked out "Love & Logic". My Mom took a class on this a couple of years ago and really liked the principles behind the approach. I've also heard good things from others who live by it's guidelines, so we'll see. We are attempting to ignore the whining, but no solution has been found for the biting. I guess I'll just read on.