I'm without access to my Monster Manual and trying to create a mind flayer. Is the creature's mind blast a special attack or a spell-like ability? I'd really like this 12 Hit Dice mind flayer to take the feat Quicken Spell-like Ability and apply the feat to its mind blast.
Both Mind blast is both a spell-like ability and a special attack.
The DnD3.5 has a category of character/monster properties called Special Abilities. They include extraordinary, spell-like, or supernatural abilities. These abilities appear in the monster entries either in Special Qualities or in Special Attack entry. It depends on the Special Ability function, whether it is used to attack or to defend. So, a character/monster property can be both a Spell-like Ability and a Special Attack at the same time.
To find out how the ability interacts with magic (including metamagic feats) you need to know whether it is extraordinary, spell-like, or supernatural. Whether it is a Special Attack or a Special Quality does not matter.
In your case mind blast is a spell-like ability and its level is not specified, so by RAW:
For creatures with spell-like abilities, a designated caster level defines how difficult it is to dispel their spell-like effects and to define any level-dependent variables (such as range and duration) the abilities might have. The creature’s caster level never affects which spell-like abilities the creature has; sometimes the given caster level is lower than the level a spellcasting character would need to cast the spell of the same name. If no caster level is specified, the caster level is equal to the creature’s Hit Dice.
(emphasis mine) link
I.e. all prerequisites for Quicken Spell-Like Ability monster feat are met
Prerequisite Spell-like ability at caster level 10th or higher.
But the description also restricts the level of the spell the spell-like ability imitates. The table in the link above lists 16th level (i.e. 16HD for mind flayer mind blast) for 4th level spell (according to mind blast description it imitates 4th level spell).
You can NOT use Quicken Spell-Like Ability monster feat with 12HD mind flayer Mind Blast. You need at least 16HD.
Whether the property is a Special Attack or a Special Quality matters when applying templates, for example.