I searched for a few months and ended up buying a rent-ready, duplex in Brookhaven, PA.

Right, but to get an ARV close to $130k, you'll probably need rent to be close to $1,300 unless you can sell it to a retail buyer, which could be a big risk on its own. 

Gross rent multiplier (GRM) A method that divides the purchase price by the gross annual rents when the property is 100% occupied.

None of these communities will be changing to residential neighborhoods, although a couple do have residential 'sides' that full time residents live in and can not be rented short term.Two of the big communities that you will have some issues with self managing are Reunion and Margaritaville.

She agreed to pay a $400/month pet fee on top of the $1,150 rent.

As far as your next property, if you are already considering moving you will get better loan options + interest rates if you decide to live in the next property and rent out your current house. 

When evaluating markets for rental properties, there are a lot of factors to consider: population growth, employment rates, rent to price ratio/GRM/Cap Rate, rent trends, vacancy rates, etc. 

You can't charge extra pet rent or even a pet deposit because it's legally not considered a pet.

If not, how much are you all "throwing away" on rent when those funds could be applied to ownership?

The property was rented and generated $160 cash flow after mortgage, taxes, insurance and property management fees were paid.