Copy table to the first unused row on another sheet

Try:

Sub CopyRange()
    Application.ScreenUpdating = False
    Dim bottomF As Long, bottomA As Long
    bottomF = Sheets("Today's Queue").Range("F" & Rows.Count).End(xlUp).Row
    bottomA = Sheets("Today's Queue").Range("A" & Rows.Count).End(xlUp).Row
    Sheets("Today's Queue").Range("A2:G" & bottomA).Copy
    Sheets("Queue History").Cells(Rows.Count, "A").End(xlUp).Offset(1, 0).PasteSpecial xlPasteValues
    Sheets("Today's Queue").Range("A2:F" & bottomF).ClearContents
    Application.CutCopyMode = False
    Application.ScreenUpdating = True
End Sub