Hi Med. Welcome from the Pacific NW
Yeah... Bathing a Doberman without using correct technique or proper shampoo can cause dry skin. Hot water is to be avoided. However, it is no big deal. Personally, with no other symptoms, I would simply lay off bathing and allow the natural oils to return. With no obvious medically related underlying causes, the dry skin should clear up shortly.
That being said... Dobe pups are prone to minor skin issues, partially because of an immune system which is slow to mature. Bacteria (eg staph), viruses (eg papillomas) and mites (eg demodex) are common causes. These skin infections may cause dandruff. However they exhibit other symptoms as well. Improper or excessive brushing can also cause skin issues by irritating the skin follicles. I do not generally brush my Dobermans.
Dobermans are short haired, single coated dogs. Their hair and skin are constantly being renewed and replaced. My opinion is that even using correct technique, bathing is best kept to a minimum, if possible. The obvious exceptions are:
-Grooming for competition
-Removing foreign or smelly residue.
Over the years (decades actually) I have found that an occasional rinsing off with cool water followed by a gentle wipe down with a clean Terry cloth towel is all that my dogs need. A healthy Doberman should not smell bad. If my dogs get a bit itchy at certain times of the year, the frequently recommended use of a dilute vinegar and water spray or rinse generally suffices. My last boy never had true bath in his entire life and his coat and skin were always heathy and beautiful. My current 9 month old girl has yet to be bathed. Our winter rains here in the PNW have given her several "natural" baths. A quick wipe down and she is good to go!
Keep updating on your handsome boy Rex.