auto copy rows to new sheets when dates are entered

My main worksheet is Job Log. All jobs are entered into this. As each step of the job is completed a date is entered into the columns headed "Quoted" is E, "Approved" is F, "Parts Ordered" is H, and "Parts In" is I. I also have sheets for "Quoted", "Approved", "Parts Ordered", and "Parts In". I would like to have Excel automatically copy the rows from the Job Log to the following sheets as the steps are complete so that at any given time I can get a list of what jobs are in what stage. So if a job has not been approved the cell in column F would be blank and only rows with a date in column F would copy to "Approved". It would also be nice if a row has an approved date it would not show on the quoted sheet because it would show on the approved sheet. Any help would be Awesome! Thanks for your help and suggestions.

This just a small sample that I am using to test the sub scripts. This file is used all years and ends up with thousands of rows in the job log. I have entered test dates into various fields to help see if the test is working. I want it to copy to the page based on last date entered. Such as if the last date entered is in the quoted column it will copy to the quoted sheet or if approved it will copy to the approved page. Thanks for all your help!!

Thanks for your help. This would not run for me. I knew how to do this 13 years ago but now I just feel stupid. Any suggestions on how to get this to work will be greatly appreciated.