@Victor Mondragon I don't know which Houston, TX you're talking about, but property tax here is anything but reasonable!
All kidding aside, I really think this is an interesting idea. I’ve been curious about this strategy myself, and it’s good to see some actual estimates for build, rents, costs, etc. At first glance, your numbers look reasonable. I tend to be more on the conservative side, so I would budget in something for a capex reserve fund, even though this is a new construction. If you plan to hold it for the long term, you're eventually going to need to replace the water heater, HVAC, roof, and all that - even if it's 10-20 years out.
Did you look at calculating a cash on cash return for this project? How much of your own funds would you have tied up in the project? If you actually are making $362/month in profit and say have $20k tied up in the deal, then your COCR would be 22%. Not bad!
And back to taxes: $6100 seems a bit low for a house in the Heights. Even assuming a 2% tax rate (with homestead exemptions?), that would put it at a valuation of about 300k. Does that sound about right? You might consider talking to an appraiser to see what your property would appraise at with the new garage apartment. Eventually they are going to tax you at the market value of the property, so taxes will creep up.
Another thing you might consider is if there is any way to maximize your potential rental income without increasing the build cost too much. For example, could you add 2 units instead of 1 for a similar build cost, but for a proportionally higher expected rent? Maybe a small studio that rents for $900 and a 1 bedroom that rents for $1300?