TL;DR
Instead of unlaoding the RMySql package, explicitly set the sqldf default driver option to SQLite before calling the sqldf function:
options(sqldf.driver = "SQLite")
sqldf("select * from df limit 6")
Explanation
If not explicitly defined, the sqldf package decides which DB driver to use as follows:
If not specified then the "dbDriver" option is checked and if that is not
set then sqldf checks whether RPostgreSQL, RMySQL or RH2 is
loaded in that order and the driver corresponding to the first one
found is used. If none are loaded then "SQLite" is used. dbname=NULL
causes the default to be used.
In your case, RMySql has already been loaded and sqldf will try to use the MySQL DB and write into a schema called test. Detaching and unloading the RMySQL package is one option, but not necessary. As mentioned by @GaborGrothendieck in his comment, the easiest fix is to simply tell sqldf which DB driver to use explicitly, i.e.
sqldf("select * from df limit 6", drv="SQLite")
To not always having to add drv="SQLite", you can permanently set the default driver for the session to SQLite:
options(sqldf.driver = "SQLite")