I've been researching heraldry in the Holy Roman Empire and I wonder if there are any coats of arms or even symbols for duchies and/or families in the 9th, 10th or 11th century? For example the duchy of Bavaria or King Otto I.?
Not really. Heraldry as you seem to have found out doesn't really exist in the Early Middle Ages, it is a much later development.
Now there were coats of arms that were attributed to figures from the Early Middle Ages, and before, and I've written about them before, so I'll borrow from that answer a bit:
Symbols of royal authority at this time tended to not be reproducible symbols that should be used on banners or flags, but were instead more...unique. Specific gifts given to followers, elements of romanitas (aping the customs and trappings of Ancient Imperial Rome), royal estates, and so on were all much more immediate stand ins for royal power. However as the Medieval period wore on, and especially as the influence of chivalric orders and poetry, heraldry, and increasing literacy, gained in prominence across the Medieval world of western Europe coats of arms were created or attributed to past rulers from Homeric, Biblical, Classical, and early Medieval times.
The history of the arms attributed to Arthur are actually tied up within the history of the "9 Worthies" who were 3 pagans, 3 Jews, and 3 Christian rulers who were believed to encompass medieval chivalric virtues. The three individuals were as follows~
Pagans
-Alexander the Great (who was incredibly popular as a figure in medieval romance stories. These stories often bore little semblance to reality, but their popularity was through the roof. According to some of these mansucript traditions, Alexander traveled in balloons drawn by griffons, sailed inside a submarine, built walls to keep demons out of Asia, fought Amazons and all sorts of creatures, in addition to his already impeccable military credentials.) The great king of Macedon was given, in heraldic terms, Or a lion gules armed and langued azure
-Julius Caesar was given Or a double-headed eagle displayed sable, which the keen viewer may note was the same coat of arms that the (Holy) Roman Empire is associated with. A double headed eagle on a golden background.
-Hector of Troy was assigned Gules a lion or armed and tongued argent maintaining an halbard argent shafted azure
Jews
-Joshua, Or drake verdant
-King David was given, unsurprisingly, Azure a harp or
-Judah Maccabee was assigned, Or two sable martlets addorsed and elevated
Christians
-Godfrey of Bouillon, was given the coat of arms of Jerusalem, the kingdom that he technically did not found as he was never crowned king of Jerusalem because of his objections to being titled king, Argent a cross potent between four crosslets or
-Charlemagne, was given a combination of the two realms he helped found, France and Germany, or, in sticking with the theme of heraldic terminology, Per pale the Holy Roman Empire and France He is in the bottom right
-King Arthur was attributed Azure (sometimes gules) three crowns or
Now these attributed arms were not always consistent, as there were different traditions which mixed and matched these arms and provided different ones as well! Here are some examples.
(There are also interesting cases where the coats of arms are conflated. For example, there is at least one manuscript from the 15th century that deliberately gives Alexander the Great the arms of King Arthur! I believe this was due to the romance having been commissioned for or by the English royal family and an attempt to extol he military virtue of the then king of England, Henry V..... But that is still just speculation on my part)
