If the difference in floor heights is significant (and 1/2" sound like it could be), you might look at thresholds for exterior doors. They come in oak as well as metal and some designs will accommodate different floor levels. Be sure to measure your door between the jambs before you go to the hardware store or lumber yard so you know how wide it needs to be. You'll still need to cut it down to fit.
If you have not installed a threshold before, there are some tricks. Please let me know if you need that additional information.