I have heard the same thing: SQF Level 1 is not GFSI benchmarked. SQF Level 2 addresses food safety programs. Level 3 adds requirements for a food quality program. Based on my experiences with obtain SQF Level 2 certification where I work, the jump from Level 1 to Level 2 is huge. The jump from Level 2 to Level 3 is not that bad but depends on whether you already have a documented quality program. Level 2 and Level 3 require a lot of documented procedures, policies, meeting minutes, management review, etc.
You would have to check with your certification body about changing the scope from Level 1 to Level 2. If you have not set up an audit date with a certification body, you will probably not have enough time. Depending on your certification body, they may be booked for the next six months or more.