Sorry, but we don't know that you don't want to do this unless you tell us exactly why - so I'm permitted to ignore that.
There lots of ways to do this:
o Go to Tools | Options... | LibreOffice Writer | Table | Input in tables, and ensure "Number recognition" is ticked.
o Enter your data as genuine dates.
o Format your data using Table | Number Format...; choose Date under Category and December under Format (or Format code NNNN for days). Note that the appearance of your table is now exactly as you wanted it.
o Sort your values normally, using Numeric for "Key type".
o Copy your table (text) data (or parts of it) to a spreadsheet.
o Sort the material in the spreadsheet. On the Options tab of the Sort dialogue, tick "Custom sort order" and select "January,February,March...". (Days are also available.)
o Copy the sorted material back to your table in Writer.
o Copy your table (text) data (or parts of it) to a spreadsheet.
o Convert values there to genuine dates, using available functions.
o Sort the material in the spreadsheet (using normal numeric sort).
o Either freeze the date values back to text, using TEXT(), and copy the results back into your Writer table,
o Or copy the date values back and format them appropriately there.
There are probably more ...
I trust this helps.
Brian Barker