I looked at the help and it seemed to say, that I need to build the building and get a mercenary license. But than I read somewhere else that the license was just needed for when you maxed out the academy level wise. 

Don't have license and theres no "make new squad" option on pet list menu. 

I need a license don't I?

Update: Was trying to organize the pets into groups based on species (just so I could keep track better), and than saw the "upgrade to squad" button. 

I didn't realize this before as I never managed the "groups" button before. 

Oops:P

I think you already figured it out, but I guess I'll clarify if you need it. :)

As you've already found out, you can create squads by going to your groups. Only four pets per squad, and one squad is in one group. For now, you have a lv1 Military Academy, so you can have one squad. Lv2 and lv3 mean you can have 1 more or 2 more squads respectively. 

Military Academy lv3 is the highest level you can achieve, meaning you can only have 3 squads via the building. However, if you want more than 3 squads, you can get a Mercenary License. It is a premium shop item, meaning you buy it with gold. One mercenary license equals one more squad.