There is the open-form compound word clothes shopping:
Realistically, before embarking on this journey I thought that quitting clothes shopping might help me clear a few bucks from my credit card.
- The Sydney Morning Herald
As English is a productive language, consider the variant ‘word shopping’ to be a ‘single’ (open compound) word synonym to single-word-request.
The parallel to clothes shopping includes
- having a good idea of the context (person / sentence);
- not necessarily knowing what it would be beforehand; and
- knowing a good fit upon seeing it
One might extend the analogy to having someone else produce the item, or paying for it (via rep points), but these are incidental.
The sample sentence, as given, doesn’t lend itself immediately to this term, but you might say:
- It's time to go word shopping at EL&U!
Admittedly, this is a somewhat cheeky answer. If open compound words are to be considered, single-word request already fits the bill. :)