This is not authorized, since the government does not deem personal pets as a reimbursable expense or entitlement (see attachment, Joint Travel Regulation pg. U3B-2).
However, I suggest the following COAs:
1-The SM can arrange transportation via BWI customer service representative POC is Mr. Steele @ (410) 918-6900 on a later date. Mr. Steele has informed me that the next available pet vacancy slot is o/a August.
2-Arrange transportation to ship pet via commercial airlines
3-Opt to leave pet w/ family member.
Standing by, if anyone has additional questions or concerns.