First you need to decide if you want your border fabric to be one long solid piece or pieced sections. One long piece would give you left over fabric to use for something else. Pieced would use up most of the fabric. Also if doing mitered corners that takes more fabric too. That makes a big difference in the amount of fabric you'll need.
I have Diane's book (Creating the Native American Star Quilt). In it she shows adding "length panels" to most of her quilts. The "Turtle" picture you show has white length panels added to top & bottom. According to the book length panels are cut at 5 1/2" x 60" each. This would add 10" to the length of your medallion. The medallion would then be 60" x 70".
It also looks like the light green border is top & bottom only, actually another length panel at 5" each. It also looks like she used the light green as binding too.
Diane's book shows piecing the boarders. She shows a Queen finished at 90"x100". Your batting isn't big enough for that tho. At best you'd end up with a finished quilt at 82" or 84" x 100". If you want your quilt to finish at 90" x 100" then you need to get bigger batting.
If you draw this out on paper it will make more sense to you.
If you purchase "backing fabric" you'd need 3 yards at 100" wide.
If you can give a little more info we can figure this out for you right down to the cuts.