Wow- our kids should hang out. My daughter did the same thing with rolling over, crawling, and now with putting on her shoes- she's only 20 months old and I keep telling her "don't stress, you're not supposed to be able to do that yet!" but she stands in the middle of the living room just pushing her foot into her shoes and screaming. Now she can do it, and I'm like, "hey, why not." But this is totally normal, and the phrase "terrible twos" is misleading. A) It actually starts around 18 months (and even earlier for more advanced kids), and B) I prefer to call it the terrific twos for a lot of reasons. First, "terrible twos" is such an awful name for a really wonderful period of development, and giving it that name makes parents approach it negatively. I LOVE LOVE LOVE this age- they learn so much it's amazing, and they really begin to interact with you.
For starters, you're absolutely on the right track because you already understand that she is frustrated because she doesn't have the words to tell you how she feels or what she wants. The keys to surviving this is to A) NEVER NEVER NEVER not even once give in to a tantrum. It doesn't matter what she wants, food, drink, whatever, you are not a bad person if you wait for her to calm down to give it to her. And don't hold or pick her up, either, at least in most cases. Of course, if she's hurt or sick it's a different story, but we know our kids. We know the difference. From the age of one I have insisted that my daughter use some form of communication OTHER than whining or crying (only because she was able to) when she wanted something. At first when her vocabulary was limited she only had to say please and point (and only because she had already learned please), and I would say "you want a drink please" which helps to make her feel less frustrated because it shows I understand her, and helps to develop her vocabulary. And when I say no to her and she throws a fit I ignore. I don't try to distract, I don't give in, I just ignore. Now that she's older and I can reasonably expect her to know crying when I say no isn't okay, I put her in time out if she cries for long, but I wouldn't do that until she's closer to 2.
I'm kind of a rambler, so here's a simplified list of tips
1) Give her the words (say it for her, even if you aren't going to give it to her, because sometime just knowing you understand helps)
2) When you know she can say it, insist that she say it versus whining. And be firm about it. Say "you're a big girl, and big girls use words. I'm not going to give you your _____ until you use words."
3) Encourage her to do the things she is determined to do, and console her when she gets frustrated. Teach her to say "help."
4) Be firm and don't ever ever EVER EVER give in to a fit. Repeat the no (and why if possible) and then ignore. If you're in a store, ignore. I know that's the hardest part, but no one's going to judge, and if they do they obviously don't have kids, so who cares!
5) Try to negate fits and tantrums by keeping her on a routine and by making sure her basic needs are met- food and sleep are big ones that can trigger meltdowns.
Lastly, two books that helped me a great deal with this stage- "The Happiest Toddler on the Block" by Dr. Harvey Karp, and "Your Child at Play: Ages 1-2." (I don't know the author). I don't do the "toddler-ese" Dr. Karp recommends, and I really don't know why, but just reading the book helped me understand a lot about toddlers. And "Your Child At Play" is such a great book for moms- it's mostly about the things that interest children at this age, but knowing this and the way their little minds are working is wonderfully inciteful, and it has lots of wonderful ideas for simple toys and activities that I can almost guarantee will keep toddlers occupied for, well, longer than 5 minutes! For example, it suggested cutting a hole in the top of an oatmeal container instead of a store bought shape sorter- more things can fit in it and since kids this age are really too young to learn shapes, they can work on more age appropriate concepts like "what will fit in this hole?" and "why doesn't the big block fit but the little one does?"
PS I just re-read your request; no, she's not doing it for attention, but you have to continue to ignore! If you give in then she will learn that she gets attention, and then she WILL start doing it for attention. My daughter still throws fits, but despite her high spirits she is much more cooperative and throws a lot fewer fits than some of her playmates whose parents don't have as much follow through.