Will under eye fillers help with these dark circles and fine lines?

In my opinion you're a great candidate for a Hyaluronic Acid based filler in this area.  It would help eliminate the shadowing and give you a more rested appearance.  I find that filler in this area, when done correctly, tends to last a very long time.  Thanks for including a picture with your question! 

A combination approach will give the most improvement. Fillers, lasers, and microneedling/PRP can improve under the eyes. My patients try to get non surgical treatments to avoid surgery. We use PRP and stem cells there often. I suggest consulting with an expert to develop a treatment plan best suited for your short and long term goals. Best, Dr. Emer