ETA: but we don't know why Quirrel would do that; see discussion below.
Misdirection? The scenario would go like this: ideally, Bella is found dead, and chucked out as just another Azkaban victim.
In the event anyone is suspicious and does some checking, the easiest thing to do would be to inspect the contents of the cell, immediately uncovering the poison. (If you were suspicious, it would take you a long time to work down the list of suspiciousness to 'a genius wizard used an incredibly advanced spell to create an identical dead body'.)
Instantly, the investigating Auror's mind deduces that someone good wanted Bella dead, and unable or unwilling to use the Killing Curse (stealth), used an alternative method (poison).
This is even wronger a theory than just being suspicious, and it's completely contradictory to a escape theory (because the investigator has to postulate someone on the level above seeking to manipulate them before the presence of poison has an explanation), so it's even less likely anyone will wonder whether it's the real Bellatrix and check for the dummy.
- This thread has run its course. You will find newer threads in the discussion section.
Another discussion thread - the fourth - has reached the (arbitrary?) 500 comments threshold, so it's time for a new thread for Eliezer Yudkowsky's widely-praised Harry Potter fanfic.
Most of the paratext and fan-made resources are listed on Mr. LessWrong's author page. There is also AdeleneDawner's collection of most of the previously-published Author's Notes.
Older threads: one, two, three, four. By tag.
Newer threads are in the Discussion section, starting from Part 6.
Spoiler policy as suggested by Unnamed and approved by Eliezer, me, and at least three other upmodders:
It would also be quite sensible and welcome to continue the practice of declaring at the top of your post which chapters you are about to discuss, especially for newly-published ones, so that people who haven't yet seen them can stop reading in time.