Some things to think about:
In order to become a base recognized organization, there needs to be at least a president and a treasuer, all other positions are extras but you must have a president and treasuer.
The organization should be self sustaining, the base typically does not pay for these type of organizations.
Also, there has to be no other organization like this, so you may want to talk to the Carney Park Dog Owners Association, as they are base recognized, to make sure you are not overlapping (that would cause the recognition to be denied.)
that is their info on facebook for those that do not know or may like to join.
Also think of what you want this organization to do. For instance, do you want this organization putting together events like play dates for dogs, animal events, volunteer work, fundraising events? What is the purpose, function and responsibilites of such an organization?? All of this will have to be documented for base recogonition.
Holding a meeting would be a good start.