My youngest daughter had a dummy until she was 4. I thought I'd never prize the thing out of her!
In the end, I had a brainwave and said there was a baby monkey at the zoo whose mummy couldn't get any sleep because he had no dummy. We wrapped it up in parcel paper and posted it to "The baby monkey without a dummy, London Zoo, England". I often wished I could have been in their post room the next day!
Annie, I wouldn't be concerned about Ezzie's thumb sucking. She'll grow out of it. The wonderful thing about having them young is that you get to see them grow up over the years... She won't be doing it when she's six, and you'll probably wish she still did in a way.
(BTW, it's also probably partly due to the salts in your skin that she likes the taste of as well.
)