Dorothy Louise Gage was born June 11, 1898 and died November 11, 1898 at exactly five months old. L. Frank Baum loved children very much, but Dorothy was also greatly loved by her Aunt Maud as well.
The main reason for why I think the little Gage girl was the inspiration of Dorothy Gale, is because Baum dedicated The Wonderful Wizard of Oz to Maud, who said that Dorothy Gage "was a perfectly baby. I could have taken her for my very own and loved her devotedly." (Perhaps this was a basis for Dorothy living with her Aunt Em and Uncle Henry?) So could the Gale girl have replaced the Gage girl? With a one-letter swap in the last name, it seems obvious.
In memoriam, I found three photos of her two headstones...
This is the original headstone. For those who prefer reading text, here's what it reads:
DOROTHY
LOUISE
DAU. OF
MR. & MRS.
T.C. GAGE
JUNE 11, 1898
NOV. 11, 1898
LOUISE
DAU. OF
MR. & MRS.
T.C. GAGE
JUNE 11, 1898
NOV. 11, 1898
This headstone was purchased by some "Munchkins," the photo description read. I am assuming it meant the Members of The International Wizard of Oz Club in the Eastern area of the United States. (Although, it would be interesting, but unlikely, if the little people from the MGM movie were responsible.)
EDIT: Jane Albright informs me that MGM "Munchkin Mickey Carroll was responsible for the foot stone marking the infant Dorothy's grave. His family has been in the monument business for generations, and when he heard this grave had been found he was quite determined -- and generous -- in insisting that he would be honored to provide a stone explaining her association with Oz."
More information can be found here. (Thanks, Jane!)
The new headstone reads
DOROTHY LOUISE GAGE
JUNE 11, 1898
NOVEMBER 11, 1898
NIECE OF
MR. & MRS. L. FRANK BAUM
NAMESAKE FOR DOROTHY
IN THE WIZARD OF OZ
JUNE 11, 1898
NOVEMBER 11, 1898
NIECE OF
MR. & MRS. L. FRANK BAUM
NAMESAKE FOR DOROTHY
IN THE WIZARD OF OZ
Personally, I find that the little girl died at such a young age to be very sad. But, unfortunately, deaths for very young children were common before we entered the age of advanced medicine. (Perhaps this is one reason why Baum eliminated death in Oz?) Thus, it was common for parents to have large families. L. Frank Baum himself was part of a large family, and was almost a casualty of poor health himself. (So was I, come to think of it.) Perhaps Baum felt connected to Dorothy, in that he almost shared her fate...