Ok, so I was just in the middle of working on a CR 9 construct with 12 HD, which would give a normal monster 6 feats, but then looking at the golems in the Bestiary, I noticed they don't have any feats. Is this due to a lack of intelligence score? Or do constructs just not get feats anyways?
Mindless creatures only get bonus feats (for example, all Skeletons have Improved Initiative, and ONLY Improved Initiative). They do not get feats from hit dice.
Some constructs are actually intelligent, so some do have feats.
Mindless creatures do not get feats from their hit dice. They can still get bonus feats (for example, Skeletons have Improved Initiative as a bonus feat despite being mindless and losing any feats they normally would have).
Not all constructs are mindless, so if you want to give your creation an intelligence score, that lets it have feats from hit dice. Or you can just give it feats as bonus feats, although to keep in theme you'd want to keep those to inherent properties (such as Improved Initiative or Toughness) rather than extra abilities (such as Whirlwind Attack).