Facings should always be stabilized in any garment. A good fusible interfacing (not the cheap stuff) will work. Also, you may want to reinforce the stitching at the v-neck by sewing it twice. I believe it is Nancy Zieman who recommends when sewing a v-neck to start at the neckline, come down to the v & go one stitch past. Then on the other side, start at the neckline, come down to the v & let the seams intersect by one stitch. Back stitch each seam at the v point for reinforcement. Then clip close to the edge on each side of the seam allowance to remove the excess fabric. Hope you can understand this.
Marty

Brighten each corner where you are ... smile!