VBA code to pull data between sheets on a condition of column K

I am creating a workbook that has 12 sheets, January - December.

I would like to have the data from January to automatically go pull into the March, May, July, September, November sheets if there is not a date in column K.

I currently have this set up with a formula for each line. For instance, the cells in March with the formula [=IF(+January!K3="",January!A3:B4,""] to pull the data over from January, however, if a row needs to be inserted, it automatically throws everything below it off. Another problem, is that if a date is entered in column K, then it just leaves empty rows in the spot it would pull from the previous 60 days. Again, if those are taken out, it throws an error. I am not sure what I need to do to first.. Do I need a macro for this? or a condition?

I attached a sample of what I'm working on to view. Any input you may have on this will be extremely helpful

title updated.