I strongly recommend your tester call the school and explain the situation. Ask your tester if the school's plan to wait for a few weeks is acceptable. Ask your tester to contact the school and start building a relationship. It's much less ego-threatening for the school to hear it from an expert than from a parent.
One problem to be aware of is that - without guidance from an outranking party - the school is set up to test up to grade level, or perhaps a level above grade level and then they will stop. Challenging all children isn't part of the mentality and expectation for all schools, and though many will accommodate after you help them see just how unusual the child in question is. Which they can't do if they don't look for it - so that is the role of the parent or parent-proxy.
So I would see what the tester says and try to secure agreement to get the ball rolling now, if possible.
I would also - if it looks like you'll just have to wait, be very very specific that the tester said 3rd grade and you want the child tested with 3rd grade reading tests. If the tester won't do it, then you do - in writing as a formal request. It's too easy to put off a parent over the phone or email.
Now is also a good time to read up on the district's policy on acceleration, gifted, scope and sequence to see what is expected of each grade. See if there is a 'school motto' that you can use to couch your requests. Read, "Getting to Yes"
Smiles,
Grinity
