There are advantages to refinancing early. For one, you are not extending your home repayment by too much. And if you exchange a 30-year loan for a 15-year one, you're actually shortening the repayment period. But you might want to consider other options besides FHA. For one thing, if you refinance into a new FHA home loan, you pay mortgage insurance premiums no matter how much your value increases. So it probably won't make sense to have that loan for 15 years
Before streamlining into another FHA loan, check out your property value. Get some comparisons from lenders -- FHA versus conventional (non-government) products. Especially if you have good credit, a Fannie Mae or Freddie Mac mortgage might save you a lot in mortgage insurance premiums and provide a lower rate as well.