First, I'm a lot older than you, and my background is in real estate, so I am comfortable with investing in real estate. Not everyone is suited to be a landlord, and you will have to think about that as well as the financial aspects.
Having said that, I do not know enough about your property to tell you what I would do if I were in your shoes. You indicate your mortgage payment would be $1,934 if you refinanced to a 15 year loan. You don't say whether that includes taxes and insurance and you have not said whether there is an HOA. Also, I have no idea what market rent is. However, even without that information, I would give some thought to holding on to this property as a rental. Here's why.
1. You already own this property. There are no acquisition costs to pay before putting this asset in service. However, selling this asset involves substantial disposal costs. The transaction costs can exceed 7 or 8 percent of property value, depending on commission, transfer taxes, title insurance, and settlement costs. That's money out of your pocket.
2. You are in a financing environment that is historic in nature. Never have I seen interest rates this low and I don't think we will see them again in my lifetime. You have the opportunity to refinance this property today at an owner occupied interest rate of 3.5 percent or less for 30 years and 2.875 percent or less for 15 years. I would not pass up this opportunity to leverage something I wanted to rent out in 5 to 7 years at today's owner-occupied rates. The leverage may be what makes this plan feasible, especially if you go for the 30 year loan.
3. You live in an area where employment is likely going to go up. The federal government (and all of its' contractors) is not an employer that will shrink anytime soon. Over time, rents and values will likely continue to increase. If you live in a neighborhood with good schools, easy access to public transit, and a low crime rate, the rent and value of your property will go up as fast or faster than the average. Demand for rentals will be high because of the high and increasing cost of buying. Prices and rents could be substantially higher when you are ready to move.
4. You will likely qualify to shelter some or all of the income from this property once you convert it to rental use. Talk to your tax person about this.
5. If you refinance today and rent in 5 to 7 years, your tenants will likely be paying for the house until you are ready to retire in the 9 to 12 year time frame after that. During that time, you will benefit from the equity build-up through mortgage paydown by your tenants, as well as any appreciation in property value that occurs. You can decide to sell the property to pull out the equity or keep it as a rental when you retire.
To determine if this makes financial sense, you need to know what market rent is for your property today and what all of your expenses would be if you were to rent it out now. If the net cash flow is hugely negative, this idea may not make sense, even with a stabilized low interest loan payment. However, if the numbers are not that far off, in your shoes, I would keep this plan on the menu, refinance, and re-examine the situation as I got closer to buying a new house.