First, having no credit is NOT the same as bad credit. Don't let anybody tell you otherwise - they are lying. The huge difference is:
Having bad credit (credit scores below 650) means the person either doesn't pay their bills on time; owes more debt than they can handle (their income is not enough to pay the bills) or they have a foreclosure, short sale or judgement against them.
Having no credit means you can just open a credit card or 2, charge very small amounts to it and pay the bill in full at the end of the month. Within 2 months, you will have a credit score and you can use that credit score to rent an apartment.
Your bigger issue is the one shot deal and your budget of $1,800. Your best bet is a studio or 1 bedroom. A 2 bedroom in Nassau County is over $2,000./month. I would look in places like Hempstead, Floral Park, Franklin Sq., Uniondale, Freeport, Rockville Centre, etc. I know these are not the best areas, but you need to realize that a 1 bedroom apartment in the better neighborhoods will be over $2,000./month and a 2 bedroom rents for about $3,000./month.