You can sell your current home at any time - it would be up to the buyer to determine how they want to finance the purchase. You would then go out and purchase the new home (since you would no longer be a first-time home buyer, you may not qualify for an FHA mortgage on the new home).
In any case, I would suggest saving up money - if the house you are in cost $283 and you owe $265, assuming the house still appraises for the same price, your equity is $18,000...your costs to sell the house will be between 9 and 10% (real estate commission and closing costs) which means it will cost you $28,000 to sell the house, meaning you will have to come up with $10K just to sell the house. You would then be expected to come up with a minimum of 10% (of you can even find a lender willing to accept a 10% down payment) and more likely 15 - 20% for a down payment and an additional 5% for closing costs.
And just so you know, you don't convert an FHA loan to conventional, you refinance - to re-finance, you are most likely going to need at least 10% equity in your house and more likely 20% which means at the current balance, your house would have to appraise at about $295K just to get to 10% equity so you could re-finance (and most lenders want 20% equity).