The best clue we have is when Olivia and Peter are talking about faith:
Peter: You're obviously a believer.
Olivia: My mother believed in God, but all the praying in the world didn't stop my stepfather from terrorising her, and her faith just seemed to put her in harm's way.
The nonchalant way she talks about her abusive childhood suggests this takes place after season 1 episode 6, "The Cure", when she first tells Peter about this. This obviously isn't much of a clue, but it's something.
Out-of-universe, the production code has a boring explanation. This article has some quotes from cast and crew explaining the situation. Anna Torv explains the production code:
["Unearthed"] was the last episode that we shot, but that wasn't the finale
Joshua Jackson explains why the episode exists at all:
"[It's] for boring reasons," Jackson said in a separate interview. "They only had 22 airdates for our show this year, but they ordered 23 episodes, so we shot one for next year, which is just silly TV network stuff.
Truthfully, since Fringe wasn't really getting into multi-episode arcs in its first season, "Unearthed" could fit in almost anywhere.
EDIT: Another thought occurred to me, although it's an out-of-universe one. I went looking at original air dates, and found that Fringe took occasional breaks in its one-episode-per-week schedule. It's not unreasonable to imagine that "Unearthed" took place over one of these breaks:
- One week gap between "The Cure" and "In Which We Meet Mr. Jones"
- Over a month between "Safe" and "Bound" (One aired in early December, the other in late January). However, we can discount this gap because "Safe" ended with Olivia being kidnapped by ZFT
- Over a month between "Ability" (Aired in early February) and "Inner Child" (Early April)
I'm going to stress that in season 1 Fringe was still presented as a wonky police procedural, with very little of the overarching mythology that would later characterize the show; the upshot is that a story like "Unearthed", which doesn't reference any of the larger arcs, could fit in basically anywhere. These are only some possibilities, with no strong evidence to support them.
Having since re-watched most of the show (using all that free time I don't have), I can confirm that the show seems to be largely following it's own airing schedule in-universe. Frequent references to the previous episode are framed as "last week's case", and in season 3 episode 14, "6B", Walter says:
Walter: It has been weeks without any new cases, which has somehow translated into never seeing Olivia.
Episode 14 aired exactly 7 days after episode 13, but episode 13 was set in the Red Universe (a.k.a. Over There, and also the first Red Universe episode since the Olivia switched back), while episode 12 (which aired a week before that) was once again set in the Blue Universe (Over Here). So I'm going to call this my official theory, although below is some interesting evidence to the contrary.
The Fringepedia page for the episode presents some interesting evidence for the theory that "Unearthed" doesn't actually fit into the timeline at all, and is actually set in an alternate timeline (Though clearly not the Red universe: Peter exists, Walter is still crazy, Astrid isn't autistic, etc.):
- We get a quick glimpse at Rusk's military record (Pic) stating he was born in 1981. Since he claims to have been married for twenty years, this suggests the episode takes place no earlier than 2019
- We also get a look at Lisa's FBI file (Pic), stating she was born in 1982. Her age is specifically said to be 17 during the episode, dating the episode to 1999
Obviously these facts are incompatible, and were most likely just prop department errors. Of course, Fringe being Fringe, things aren't always what they seem.
However as far as I know there's been no official word from the cast or crew.