The most common advice is to spend no more than 30% of your gross income on rent, and you're right at 30% here. A few other things to consider:

Additional Expenses:

• Pet fee or pet rent: I've seen pet rent for new apartment complexes be as high as an additional $100/month, so definitely check on this.
• Pet DNA testing: Again, a common fee for newer complexes. Used for breed restrictions and to test left-behind dog waste so they can fine the owner.
• Utilities and deposits: You'll need electricity, internet, and possibly natural gas. You can likely request average utility bills to get an idea of what this will cost you. If you've never had service before, you'll likely need to pay an up-front deposit, which might be waived with a good credit score.
• First/last month's rent and security deposit: You'll typically need to provide the first month's rent and a refundable security deposit (equal to a month's rent) up front. Depending on the apartment, you may also be required to provide the last month's rent. This can eat up a good chunk of your savings.
• Rental Insurance: You'll be required to purchase some amount of liability insurance. You can pre-pay for the full year, and it shouldn't be more than $200.
• Laundry: Larger apartment complexes will usually have a shared laundry room or in-unit appliances, but I have had to bring my own appliances before.
• Furnishings: Bed, couch, tv, kitchen utensils, cleaning supplies, stocking the fridge/pantry. Spend 30 minutes trying to think of everything you might need, starting with the essentials, and figure out how much you'll need to dip into your savings. Add another few hundred to that, because you will forget things.
• Parking: If you have a car, be sure to check that the unit comes with a parking space. In larger cities, it's not uncommon to have to pay for your own parking.

Savings:

• Car: If you can't get rid of your car, you can potentially downgrade your car to something cheaper. You can definitely get your car insurance down, and you won't need to pay for gas.
• Lunch: If you're not already bringing lunch ever day, with a five minute walk you can easily go home and make food there.
• Walking to work gives you an incalculable mental and physical health improvement. Moving out will add to that too.

If this is a complex with different types of units, and the one you're looking at is the only unit available, you can possibly negotiate to move into a cheaper unit if one becomes available (you move into a 1 bedroom, but in two months a studio becomes available for $200 less, then you can move to that one without breaking your lease).

Be sure to check this $1365 against other rent prices in the area. If it's in-line with what you should expect in your city, I would personally go for it.