There is no worksheet event that can trigger when a row is inserted, so you would have to code a procedure that a user could run to insert a row and copy formulas.
What version of Excel are you using?
What columns contain the formulas?
By protected formulae, I assume you mean the worksheets has protection turned on. Is the protection password protected?
This code should work, althought it might require some modification based on your version of Excel and protection options you have set.
.Copy 'copies the row that contains the upper left cell of the selection
.Offset(1, 0).Insert Shift:=xlDown
.Offset(1, 0).SpecialCells(xlCellTypeConstants, 23).ClearContents 'Clear constants in new row
ActiveSheet.Protect DrawingObjects:=True, Contents:=True, Scenarios:=True 'XL 2007 default worksheet protection