Time out was extremely effective at this age for my son. Most of his time outs when he was that young were only 30 to 60 seconds or so. The rule of thumb is a minute for each year they are. The act of doing it and letting them know it's not going to fly went a long, long way.
I was fortunate that when we started time outs, he had already witnesses other kids and I'm sure himself at daycare. He pretty much taught us. I would take your daughter by the hand and set her against the wall on the floor. I would sit down with her and look her straight in the eye and calmly tell her, "We are in time out because you were ... We do not do that and we have to sit in time out." I then would look to the floor and take eye contact away and start the count down. When the time was up, I would relook her in the eye and tell her again why we were in time out and say, "Time out's over. I need some BIG loves and hugs." And we would give great big hugs and resume.
Now, there was a time or two or more with my son that screaming and crying interfered with things. I would start with showing him how to breath deep and catch his breath and teaching him how to sigh and express how he's feeling. Most of the time, we could go to the location where time out was going to be held, and I would stop and just hold him and hug him and calm things down. Then we would proceed. Sometimes, time out was all screams. The process has to be gone through though. It may take several time before she understands, but she'll get it and a lot quicker than you think. You MUST be consistent and never threaten time out, just do it. I'll never forget about that age in a department store. My son was ready to run around like a chicken with his head cut off. We did our time out right there next to the clothes rack. It was maybe a whole 10 seconds. He got up and started running around again. We did it again. I took a couple times, but that's the only time he has ever misbehaved out shopping. He's now three and a half.