You do have a bit of a trade-off here, though. A light-weight 16" is going to be much easier to learn to ride without training wheels. She can put her feet down if she panics, she won't have any trouble reaching anything. If you get a bigger bike, it may last longer, but it may take longer for her to get independent of the training wheels. My bias, particularly if you've got anyone else to hand the bike down too, would be to get a used, lightweight 16", let her learn on that, and then get her a bigger bike when she's grown a bit and gotten comfortable riding. You could even make it a prize for mastery of the smaller bike. I know that's a more expensive option, though.
I went through this with 12" bikes. I decided to buy a fancy light-weight 12" even though it has a really short lifespan. My son learned to ride that bike without training wheels at 3, and at 4.5 he's a really good rider on a 16". We really enjoy biking together around Chicago. Meanwhile, my daughter is learning to ride on the 12", and I'm sure she'll be riding independently by her 3rd birthday. Does it really matter that that bike made it easier to learn without training wheels at an earlier age? Was it worth it? I don't know. But I'm sure that when we're done with the bike that if it's still in reasonable shape we'll be able to sell it on Craig's list for 50% of MRSP, and we've certainly gotten a lot of joy from it in the meantime.