There’s too many variables to say if DS will have a special school placement by September.
In what context has the EP said DS needs a specialist school and has she put it in writing?
Is it following an annual review? In which case, the LA has 4 weeks from the annual review meeting to inform you if they are going to amend or not. If they aren’t going to amend, you will get the right of appeal. If they are going to amend, they must issue an amendment notice when they inform you they are going to amend. At that point you will be able to name your preferred school. Then the LA must finalise within a further 8 weeks. Once finalised, you will get the right of appeal if the LA doesn’t name your preferred placement.
Is it part of a reassessment of needs? If so, following the reassessment of needs, the LA will decide if they are going to amend or not and finalise within 14 weeks. Following this, you will get the right of appeal if the LA doesn’t amend to name your preferred placement.
If the EP has said it in another context, you should request an early review. Unfortunately, there’s no guarantee the LA will agree to an early review. If they refuse, you will need to wait for the annual review or request a reassessment of needs.
If you have to appeal, you won’t have a place for September. If you don’t have to appeal, then there’s time.