When I go to the construction tab, it only gives me one of my pregnant pets as an option to build, but obviously she's busy so she can't. If I select one of my other pets with energy to be my active, they don't show up as an option? Can anyone help me out? :<

Construction requires particular levels of certain stats (e.g. Constitution, Intuition, Agility) to build objects.

http://beastkeeper.com/recipes-list

This page has a list of required statistics for construction of all of the site's items. Your pets may not have high enough stats to build what you need.

When you want to build a building or scheme, you need a pet with the required stat at or higher than the number required. The number seen under List of Requirements on the recipe (visible either through List of Recipes or Craft & Construction under your Manor tab) is the minimum number.

Let's take the example of Blueprints: Military Academy (lvl 1). The only pet that can build the Military Academy (lvl 1) is one that has a Constitution stat greater than or equal to 60. Seen here:

My pet Rousseau could build this because his Constitution stat is 103, higher than the required minimum. Meanwhile, my pet Mystikos could not because her Constitution is 47, lower than the required minimum.