Michael
If she was born after July 1, 1911 you need to go to Kansas Vital Statics Office at this link...
http://www.kdhe.state.ks.us/vital/
Note that these records are "closed". See the description on the web page above for who may obtain a copy.
From 1861 to 1911 very few counties kept birth records. As Sheridan County was not formed until 1873, it is unlikely they have any records. You will need to contact the county clerk to see what they may have.
A possible source of a birth announcement are the microfilms of the newspapers published at the time of her birth. The microfilms are available from the Kansas State Historical Society. Here is a link to the KSHS newspaper search page. Also take a look at the interlibrary loan policies from the link on the search page...
http://www.kshs.org/library/news.htm
Dave Goldy
Overland Park, Johnson County, KS
davegoldy@swbell.net