The most recent emergency operations plan in Oklahoma is from 2019. This plan can be retrieved on the website of the Oklahoma Departement of Emergency Management at https://www.ok.gov/OEM/Programs_&_Services/Planning/index.html
The portion of the plan that deals with pets during disaster response situations is Emergency Support Function (ESF) #11, Agriculture and Natural Resources Annex. In ESF#11 (appearing on page 108 of the attached pdf), one of the stated purposes is to "provide for the safety and well-being of household pets during an emergency response or evacuation situation." The Oklahoma Department of Agriculture, Food, and Forestry (ODAFF) Animal Industry Services is responsible for oversight to and assistance with protection of household pets and non-commercial livestock in evacuations and other responses (page 112 of pdf).
Appendix 4 to ESF #11 (page 120 of pdf) is entitled, "Protection of Companion Animals and Non-Commercial Livestock." The Purpose states the following:
Provide a collaborative framework for prevention, protection, preparedness, response, and recovery efforts related to management of companion animals and non-commercial livestock during emergency events. In the majority of emergency situations these issues will be the responsibility of local jurisdictions with resource support provided through non-governmental organizations and State agencies. In multi-jurisdictional or catastrophic events, the aforementioned lead agencies may provide more direct command and management. Emergency preparedness, operations and assistance provided herein shall address all provisions set forth in the Pets Evacuation and Standards Transportation Act of 2006.
The plan even addresses issue concerning both native and non-native wildlife under "IV. Concept of Operations:"
H. Engage wildlife authorities to manage wildlife and habitat issues and address any potential public safety or disease concerns to or associated with affected wildlife.
I. Non-native wildlife may be housed in zoos, wildlife parks, and wildlife sanctuaries or with private licensed individuals. These entities can be both vulnerable resources and a threat to public safety. If such facilities exist within an emergency operation area, special plans and resources may need to be developed to address the same.