The bit one row below, and one column to the left, of the needle looks like it may be the seat - hard to tell from that angle. Be sure you are getting the right kit for your engine, with the mixture adjustment screw running through the middle of the float bowl retention nut. If it doesn't have that it is for a small flo-jet. Check that your engine type number is one of those listed.
The self-threading screw has to be just the right size (p/n 93029), and it is an American size that may be hard to get here. (Post-Edit: The screw required is an ordinary 1/4" UNC, available from any hardware store, but in Australia you are unlikely to find a self-threading one, so you would have to buy a 1/4" UNC tap and create a thread inside the seat, before inserting the screw and removing the seat.) A competent mower repair shop that deals with B&S engines should have it or be able to get it though. Don't let them try to use a randomly-selected self-tapper, or they'll ruin your carburetor body. Self-threading screws are quite different from self-tappers, even though the two terms mean the same thing - look at the picture of the screw.
Last edited by grumpy; 25/11/12 10:09 AM. Reason: Add post-edit
