Greetings Gloria,
Yes, it is feasible to transplant a larger Red Oak tree with a caliper of 4-6" and a total height of 13'. Mind you, it is going to take some work on your part to excavate the necessary minimum root ball diameter for this tree. Moreover, you need to transplant the tree when it is dormant (i.e., not during the growing season).
According to the literature, you will need a minimum root ball of 42-70 inches. Which means, you will probably need to hire a professional arborist with a mechanical tree spade to move this tree. For more information on transplanting larger trees, please refer to these publications:
http://www.forestry.iastate.edu/publications/F-359.pdf
http://www.utextension.utk.edu/publications/spfiles/sp572.pdf
Best of luck!