Do LoopUntil Slow Speed

I have written a macro which is sucessful in the sense that it does what I need. However, I ran it against my data for the first time today and it took forever. To give you an idea of the data size... my code had to loop through about 10,000 rows and move the ones that met the IF criteria to another sheet.

Can anyone provide any suggestions as to what might make my code faster? Should I take a different approach? I am definitly still wet behind the ears.

My code is below...

Dim count As Integer
count = 3
PeCount = 3

ActiveWorkbook.Worksheets("MyWorksheet").Activate

Do

If Trim(Sheets("MyWorksheet").Cells(count, 12).Value) = "1111111" Or _
Trim(Sheets("MyWorksheet").Cells(count, 12).Value) = "2222222" Or _
Trim(Sheets("MyWorksheet").Cells(count, 12).Value) = "3333333" Then

Sheets("MyWorksheet").Rows(count).Select
Selection.Cut
Sheets("YourWorksheet").Activate
Sheets("YourWorksheet").Rows(PeCount).Select
Selection.Insert Shift:=xlDown
Sheets("MyWorksheet").Activate
Sheets("MyWorksheet").Rows(count).Select
Selection.Delete Shift:=xlUp
PeCount = PeCount + 1
Else
count = count + 1
End If

Loop Until IsEmpty(Sheets("MyWorksheet").Cells(count, 2).Value)
End Sub