Depends on your particular fabric, but I would at least recommend rounding-off that inner edge. pre-cut lumber is never perfectly square on the edges, always a risk for outer edge to be lower than inner.. . . . Instead of using the quarter round . . . Also would it really be that important when using 1x3's since the edge would only be ¾".
A 1x_ frame can also bow when the fabric is applied with the necessary tension. Depending on your panel size, a brace or two across the back might be required to prevent this. If given a choice, go with poplar rather than pine. A 1x3 pine frame will twist (even without fabric) before very long. :hissyfit:'Been there, done that.
My 2 cents.