It sounds like you already have month stored as a separate variable in the df.date
data frame. If so, you could create a factor from it like so:
Haude.input$monthF <- factor(df.date$month, levels=1:12, labels=c(0.22,0.22,0.22,0.29,0.29,0.28,0.26,0.25,0.23,0.22,0.22,0.22))
However, your values seem better suited to a numeric variable rather than a factor (in R, 'factor' refers to something categorical). If that is in fact true, you could do:
values = c(0.22,0.22,0.22,0.29,0.29,0.28,0.26,0.25,0.23,0.22,0.22,0.22)
Haude.input$monthF <- values[df.date$month]