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. While global historical queries are available to both WebQAC and DocQAC, DocQAC uniquely accesses document-specific context, including the current document's content and its 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 on seen queries across both seen and unseen documents. This demonstrates its practicality for real-world DocQAC 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.