I am familiar with the expression “early days” – but what does “early doors” mean

It's Lucretius: One man's meat is another man's poison.

It was coined in the first century BC by the Latin writer Lucretius, in the form "quod ali cibus est aliis fuat acre venenum" (what is food for one man may be bitter poison to others). It was first translated into English in 1604 by the Jacobean playwright Thomas Middleton: One mans meate, is another mans poyson.

See also: Lucretius - Wikiquote

Summarising and amplifying the comments thus far, the earliest usage I can find is a 1985 Supreme Court usage...

The Supreme Court said, “This doesn't pass the laugh test; not withstanding what the Ninth Circuit says, we are not going to require that a recipient receive notice of every subpoena that has been issued in the investigation.”

For several years after that, almost all instances in Google Books seem to be in legal contexts. Interestingly, the straight face test predates it by several decades (that link has one from 1956).

In practice it does effectively mean this is laughable. Given the origins are so clearly associated with legal circles, I prefer to see it as implying this would be laughed out of court (if it ever got that far). But as StoneyB says, you can also see it as so laughable you couldn't say it with a straight face.

Any strong dismissal of someone else's point is bound to be "offensive", but arguably this particular one introduces a touch of self-referential levity (from the point of view of third-party onlookers, not the person whose position is being so derisively "laughed off").

Anyway, over 3000 written instances of pass the laugh test show that it's not at all uncommon.