The corset is necessary because the blouse is see-through, you don't want to see her cleavage. 

The materials we used are the same for the gingham dress and blouse but we know what we need to do in order to make future dresses perfect.

Even small minor details matters, that's why we are very good costume makers and ruby slipper makers.

Back in those days, corsets were commonly worn with dresses like these.

Yeah, unless MGM made the blouse with thicker fabric, you could see what is under there. 

Other costume makers these days don't use the same thin fabric as the original blouse, which is why our blouse and dress is 100% accurate to the original dress as worn by Judy Garland as Dorothy.

I love the Dorothy dress. The dress is absolutely beautiful, the blue and white checks make the dress stand out.

She had to look a few years younger than her actual age otherwise she wouldn't have got the part of Dorothy, which she desperately wanted.

Sometimes these things happen in Hollywood movies. Ralph Macchio playing a younger Daniel LaRusso in The Karate Kid series in the 80's is an example. He was already in his 20's in the first series when he played as a "kid".

Shirley Temple had the young age on her side but she would have been a disaster for The Wizard of Oz.

At the end of the day, they wanted someone who could sing and Judy Garland had the voice. She showed her acting talents and singing abilities in prior movies so she was already a star on the rise. She was so right for the part of Dorothy.