Yes, increasing your caster level does allow you to meet specific prerequisites earlier.
However, these increases would need to be increases to your caster level for that class as a whole (or increased for crafting), not increases in caster level for a specific spell. Here are a couple of examples:
Whenever a forgemaster casts a spell that targets a weapon, shield, or armor, the spell takes effect at +1 caster level.
This would not apply because the caster level increase would not be applied to crafting.
+1 caster level.
This would apply, since the caster level increase is applied at all times (and thus applies when crafting).
Wearer casts his spells at +4 caster level. Effect lasts 10 minutes.
This would not apply as it doesn't last the 8 hours of crafting, and only increases your caster level for casting spells and not crafting.
However, typically you don't need to meet the caster level prerequisite of an item in order to craft it.
From the Magic Item Creation Rules:
Note that all items have prerequisites in their descriptions. These prerequisites must be met for the item to be created. Most of the time, they take the form of spells that must be known by the item’s creator (although access through another magic item or spellcaster is allowed). The DC to create a magic item increases by 5 for each prerequisite the caster does not meet. The only exception to this is the requisite item creation feat, which is mandatory. In addition, you cannot create potions, spell-trigger, or spell-completion magic items without meeting its prerequisites.
Therefore, if an item has a caster level as a prerequisite for crafting it, you can ignore it for a +5 to the DC of crafting that item.
Note that while the base DC to craft a magic item is 5 + that items caster level, there is not usually a caster level prerequisite for a magic item (and even if there is one as a prerequisite, it may not match the item's caster level).
This means that for a level 5 wizard with Craft Wondrous Item and Haste, despite Boots of Speed having a caster level of 10, the DC for crafting them is only 15 (base 5 + caster level of 10). It is not increased to 20 because there is not caster level prerequisite for crafting it.
The exception to this is constructs, which you use as an example.
From the Construct Creation Rules:
Caster Level: Some constructs, especially the more powerful ones, require the creator to be of a certain caster level in order to craft them. Unlike some other crafting requirements, this requirement must be met in order to craft the construct, and cannot be ignored simply by increasing the DC of the skill check to craft the construct by 5.
Therefore, in order to craft a construct you need to meet any caster level prerequisites it lists in it's crafting requirements.
Here are a couple items that can increase you caster level for crafting a construct.
Golem Manual: Golem manuals are one time use items crafted for a specific golem and increase your caster level golem crafting that golem. Note that unlike constructs whose caster level requirement you can't bypass, you can bypass the caster level requirement of a Golem Manual as it's a wondrous item.
Automaton Core: You can get an automaton core by taking Improved Familiar, selecting an Automaton Familiar, and murdering it, thus obtaining it's core.† A spellcaster holding an automaton core treats her caster level as 4 higher for all purposes. This allows you to use it for crafting as well as casting.
†: I am not responsible for any consequences you GM may give you for doing this.