That dress is adorable. I love shirtdresses myself. Yes, it is more of a daytime dress.
It looks like the skirt falls to the knee, which means that at least 1 inch of heel is necessary to maintain proportion. Since the dress is more daytime, the shoes should be casual, but a more refined style would work best. Sandals or thongs with a little heel would look great. So would espadrilles and wedges.
I always accessorize with earrings, and bold earrings would look great with this dress. I think a statement necklace would be too much with a shirtdress. The sleeves look like either half (elbow length) or 3/4 length, so bold bracelets would look good also.
I hope this helps.