Query auto-completion (QAC) has been widely studied in the context of web search, yet remains underexplored for in-document search, which we term DocQAC. DocQAC aims to enhance search productivity within long documents by helping users craft faster, more precise queries, even for complex or hard-to-spell terms. Unlike traditional WebQAC systems, DocQAC can leverage rich document context, having access not only to the partially typed user query and global historical queries, but also the content of the current document itself, and crucially, the document-specific history of user query interactions. To address this setting, we propose a novel adaptive trie-guided decoding framework that uses user query prefixes to softly steer language models toward high-quality completions. Our approach introduces an adaptive penalty mechanism with tunable hyperparameters, enabling a principled trade-off between model confidence and trie-based guidance. To efficiently incorporate document context, we explore retrieval-augmented generation (RAG) and lightweight contextual document signals such as titles, keyphrases, and summaries. When applied to encoder–decoder models like T5 and BART, our trie-guided framework outperforms strong baselines and even surpasses much larger instruction-tuned models such as LLaMA-3 and Phi-3 in seen-query settings. This demonstrates its practicality for real-world DocQAC system deployments, where efficiency and scalability are critical. We evaluate our method on a newly introduced DocQAC benchmark derived from ORCAS, enriched with query–document pairs. We make both the DocQAC dataset https://bit.ly/3IGEkbH and code https://github.com/rahcode7/DocQAC publicly available.