P.G.
Yes, yes and yes! Now is the time to start teaching. Just stay calm and don't let fear of a "scene" prevent you from doing the right thing. Be prepared to walk out of a store if a tantrum starts.
I am speaking as a Mom of a 15 year old, and believe me I wish I had been a little stronger and firmer when she was two!
Before you go to the store, explain in a simple way, "we are not getting any toys today"; she may not really understand but will eventually.
Stay calm, use a flat unemotional tone when you say no, and calmly put the toy back on the shelf. Then just walk away from it; pick her up and take her with you if you have to. (That is the advantage of a two year old over a 15 year old; you can still pick them up!).
Be ready to walk out of the store if the tantrum gets out of control.
I know it sounds easier than it is; I have a very strong willed child!
Hang in there, don't take any of it personally, and don't worry about what other people in the store think!!
Otherwise you are training her to have a tantrum every time she wants something and you say no. Keep it up and the tantrums will diminish! (It won't work just the 1st or 2nd time!!).
Good luck; this too shall pass!
Pam