We were given this doll by a neighbor, but she'd lost her clothes long ago. I couldn't handle her running around naked all the time, but I wasn't confident enough to make her anything with sleeves or legs, so I went for the basic sundress.
Make the dress: Cut out a rectangle the width of her chest and long enough to cover her. Sew it into a tube, right sides together. Turn it inside out. A perfectionist would iron the seam at this point.
Make straps: Cut out long skinny rectangles the length you want the straps. You'll need to have them wide enough that you can pull them inside out.
The thickness of your fabric determines that: the thicker the fabric, the wider they must be. Sew them inside out lengthwise. I made them too skinny at first and after much anger, made new ones that I actually could turn inside out.
It helps at this point to have one of those cool things I got from my grandma that grabs the end and pulls it through, but before I discovered this, I attached a safety pin to one side and pulled it through to the other side until it was right side out. Now the seam in on the inside!
Even non-perfectionist me understands that straps work much better being ironed at this point. Might as well iron the rest of the seams as well, since you have the iron out. :)
If you want even more of the seam on the inside, you could sew one end together as well as the sides. You just need one open side to turn it inside out. Repeat this for your second strap.
Sew your straps to the sides of the tube and there's your dress!
I must apologize for the unclear photo of the dress. This is our normal view of it. And our little Kewpie Doll is much cuter than the doll anyway. :)