Hi D.. This is typical. And it is a phase that lasts quite a while. Sadly, it's mostly just something you have to "deal with." But if she really gets out of hand, you can give her a one minute time out for whining. She's simply frustrated. I'm sure she knows a few words (if not a lot more) by now and she sometimes gets confused.
Our son knew over 50 words at 16 months. But he still gets quite whiny sometimes because 1) he forgets words 2) the words aren't coming to his brain fast enough or 3) he simply does not know the right words to communicate what he wants to say.
I just normally deal with it during the day and if he whines while I'm trying to make dinner, I put on the TV or even try to give him an early evening nap just so I can get my sanity back. Plus, it's dangerous for him to whine and pull on me when I'm over the hot stove.
And honestly, the wining will get worse before it gets better. There are lots of ways that books say to help ease whining, but nothing worked with our first 2 kids. We just had to be CALM and CONSISTENT. Whenever one would whine, we'd figure out what they want first. Then before giving it to them, we'd say how one should ask for that item. For example, if our son is whining that he wants to go outside, we'd say "You want to go outside? Go outside?" Even though he knows "outside," we'd repeat it a couple of times to reinforce it.
Both our kids are advanced, so a lot of the other things books said to do didn't work simply because I think it was beneath them. For your daughter to start this behavior at 16 months, it sounds like she may be in the same boat.
Good luck...my whiny boy just woke up! :)