Before you commit to anything long term (fat, implants, or VY plasty), I would suggest using a hyaluronic acid filler such as Restylane or Juvederm first. Fillers are only temporary but they will give you some idea about what you can expect before you do anything permanent.
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I would recommend you try a hyaluronuc acid filler such as Juvederm Ultra and a few units of Botox to give you filller lips with more "lip show." By trying something that is reversible, you can see if you really do like making a change in your basic appearance before you commit to it, and in any case I don't see anything that requires surgical correction.
Juvederm comes in syringes, and you would probably want one syringe or less of Juvederm Ultra, or Beletero. If it is placed stategically rather than throughout the entire lip you will not have a duck lip. Your dermatologist will be thinking about ratio of phi which is present in well-balanced faces, and will likely want to place more filler in the lower lip than the upper.