Basically you have two options:
1. Edit the edit form manually in SPD, I would not recommend that
2. Use some kind of column permissions add-on solution, such as our free Smart List Lite
infowisesolutions.com/product.aspx

Create the Due date  as a Calculated field (e.g. [start date]+7)
And/Or
Set manage content types in the task  list
Hide that column from the Content type [item]
Create a view with the Due Date Selected