A 1 bedroom typically rents for $2,000+. in most of Brooklyn. If you want to spend less than $2,000. you will have to sacrifice on safety, living with welfare residents and crime. Your budget of $1,350. is what Section 8 offers and this is typical for city housing projects. Since you earn a good income and have a great credit score, you can afford to increase your rental budget.
Unfortunately in NYC, residents typically spend about 40%+ on their rent. If you want to get a cheaper rental, move to the suburbs. Excellent public commuter railroads to Grand Central Station and Penn Station in 30 minutes during rush hours. A 1 bedroom in the suburbs rents for $1500. - 2,000.