Carry over certain data meeting conditions from one sheet to another.

I have a workbook that has 12 sheets, January - December. I would like to have the data from January to automatically go into the March, May, July, September, November sheets if there is not a date in column K.

I currently have the cells in March with the formula [=IF(+January!K3="",January!A3:B4,""] to pull the data over, however, if a row needs to be inserted, it automatically throws everything below it off. 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.