Ok, there are several points here.
One, forget leasing. Even if you got approved, leasing is the utterly cash stupidest way to get a car. The only people for whom leasing is non stupid are people who get to deduct the costs of their vehicle as business expenses.
Next, skip new cars. With your income and it's short duration, you'd pay a lot in interest if you went that way. Go for a good used car, and get it thoroughly checked out by a good mechanic before buying.
You fail to specify the age and mileage of your current car. If it still works reasonably well, then keeping it until you have more cash to put down on a newer car would be the wisest choice.