"Dungeon-crawl" started aroundgoes back at least to 1982 and was based on similar slang phrases going back to the 1800's
The etymology, in short: On the Usenet groups that were popular among RPG and wargaming people in the early 80's, "dungeon-crawl" started as a piece of slang following the linguistic model of other "-crawl" slang phrases like "pub-crawl," which had been around since the 1800's. "Dungeon-crawl" got established over time as a commonly known term within RPG communities.
By way of references, the Oxford English Dictionary's earliest reference of "dungeon crawl" is:
dungeon crawl 1982 Re: SFRPs in net.games.frp (Usenet newsgroup) 29 Oct. "SF games lack the convenient dungeon-crawl scenario type, so more work is needed than in most AD&D campaigns."
and this construction appears to pick up on a similar compound construction of "[something]-crawl" (again from OED, emphasis mine):
crawl [in compound] b. A walk at a leisurely pace. beer-crawl, gin-crawl, pub-crawl: a slow progress from one drinking-place to another. slang. 1877 York Herald 28 Dec. "The project has been mooted in certain temperance circles for establishing a mission solely for women, who are to be searched for in their daily ‘gin crawls’."
So you are right in guessing that "it has to do with the cautious pace", in that the preceding "-crawl" phrases referred to activities that involved walking at a slow or measured pace.
(Note that the 1982 Usenet reference precedes D&D inventor Gary Gygax's use of the term in Dragon issue #112, which is the earliest reference listed as of now in the Wikipedia article.)
