You are right, there is no mention of a Major General in the "Military Bill" (or the Militia Act). However, directly after this act in the printed volume on the special session (p. 43 if you have the volume) is another ACT.

"An Act to authorize the appointment of one Major-General for the Missouri Militia.
Be it enacted by the general Assembly of the State of Missouri, as follows:
1. The Governor is hereby authorized to appoint one Major-General who shall, in time of insurrection, invasion, or war, command the entire military force in the field, and shall hold his office during good behavior.
2. The appointment of said Major-General shall be subject to the confirmation of the Senate; and should the General Assembly not be in session at the time of the appointment of said Major-General, said appointment shall be subject to confirmation at the next session thereafter.
3. The said Major-General shall be ex-officio President of the Military Board authorized to be created by an act to provide for the organization and government of the militia, approved May 13, 1861; but shall have no command, except of troops actually in the field.
This act to take effect and be in force from and after its passage
Approved May 15, 1861."