Attitude in a 1 1/2 Year Old!

I have to say that I agree in just ignoring her. If you have tried time out and it seems worse, than put her somewhere safe and let her throw a fit and just continue doing your business. She will figure out that she is not getting your attention by being naughty/throwing a fit and will resort to better behavior!! I have a very strong willed 5 year old and I do the same with her and did the same at that age too. I just tell/told her that when she was done she could talk to me, but that I wasnt going to talk to her while she was throwing a fit!! Eventually she will stop doing it!! Good luck

you could also use the distraction method, if you don't want her to have something and she persists, distract her with something else...the other tantrum will disolve.

Welcome to toddler-hood! =)
My oldest had/has an attitude, so I know what you're going through. I disagree that she is too young to be disciplined, but you have to go about it the right way. Discipline doesn't always mean spanking (I think inflicting pain is counter-intuitive); it's the way to teach her correct behavior and how to follow rules. I can't tell you what the right way is for your daughter, since every child is so different, but I have found that kids are a LOT smarter than we think.
For my oldest, I had to give him time-outs on my lap. Sure, he kicked and screamed through the whole thing, but I was consistent and he figured out he wasn't going to get away with it.
A lot of times, ignoring a tantrum is the way to go. When the tantrums start to be destructive or potentially harmful (throwing things, slamming doors), of course you'll have to intervene.
Communication is important. Use simple words to tell her what is expected of her, and why she is in trouble. For example: "No throwing toys. Be nice to toys." If she still throws the toy, say, "No throwing toys. Toy goes bye-bye now." and take the toy away. Yes, it will make her mad, but she'll get the point really fast.
Good luck! I know it's hard. I'm still figuring things out myself.

Discipline done right is a process of learning how to behave not a crime then punishment reaction. It is how we become civilized and ready to participate in our society. Your daughter is not too young for discipline. She may be too young for punishment, because she won't understand that. She understands "NO," and when you say it she doesn't like it, so she throws a temper tantrum. If she keeps it up long enough she probably gets her way. All you need to do is mean "No" when you say it. Don't give in especially if she throws a tantrum. There's no need to put her in time-out, don't react and just ignore the tantrum. If she's lying on the ground kicking and screaming, step over her and go about your business. When she's done give her a hug and tell her it's good to have her back. If she doesn't get her way from tantrums, she won't throw them very often. She will test every once in a while though just to see if it might work.

Frankly I'd go about your business and ignore her. Make sure there isn't anything in the general area that she can hurt herself on and be done until she's done. You can say something like "When your ready to talk to me like a good girl, let me know" Or something along those lines and then leave the room or do what you were doing before. Maybe even sit down and pretend to read a magazine (I'm sure it would be hard with screeming going on). She just needs to see that behavior isn't going to solicit a response from you good or bad.