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The general concept of a date line preexists Caroll. By the 17th century possible locations for the line had been proposed See Here.
People living at the same general time also recognized the notion of a date line. In 1872, Jules Verne wrote Around The World In Eighty Days in which crossing the date line is a plot point. In 1888, this map was produced showing the international date line:
There were places geographically nearby with different ideas of today. Until 1844, the Philippines were a day separated from Asia. This was due to being colonized by Spain through the Americas. In 1845 they skipped a day bringing them into line with Asia.
The International Meridian Conference in 1884 established a theoretical date line at 180 degrees. But the date line did not and does not follow this line strictly. This is not what we call the international date line.
So, the international date line already existed when Caroll was writing. The general idea had been proposed centuries earlier, and countries were changing the date line to fit their needs.