Named Entity Recognition (NER) is a fundamental task to extract key information from texts, but annotated resources are scarce for dialects. This paper introduces the first dialectal NER dataset for German, BarNER, with 161K tokens annotated on Bavarian Wikipedia articles (bar-wiki) and tweets (bar-tweet), using a schema adapted from German CoNLL 2006 and GermEval. The Bavarian dialect differs from standard German in lexical distribution, syntactic construction, and entity information. We conduct in-domain, cross-domain, sequential, and joint experiments on two Bavarian and three German corpora and present the first comprehensive NER results on Bavarian. Incorporating knowledge from the larger German NER (sub-)datasets notably improves on bar-wiki and moderately on bar-tweet. Inversely, training first on Bavarian contributes slightly to the seminal German CoNLL 2006 corpus. Moreover, with gold dialect labels on Bavarian tweets, we assess multi-task learning between five NER and two Bavarian-German dialect identification tasks and achieve NER SOTA on bar-wiki. We substantiate the necessity of our low-resource BarNER corpus and the importance of diversity in dialects, genres, and topics in enhancing model performance.