I assume you are doing her classic outfit?
For this, you have far better options than leather that are cheaper and easier to sew.
I would look for a garment weight stretch faux leather. This will be a knit fabric coated on one side with a plastic material to make it look like leather, but it will breathe and stretch like a knit fabric. These types of faux leathers are widely available, even at chain fabric stores like Joann.
Another option is wet-look spandex. This will be even more stretchy, which may not be the effect that you want, but will be shinier than most other materials.
If you can find a garment-weight non-stretch faux leather, that would be another option, though most non-stretch faux leathers available in chain stores are a bit heavier in weight than what you would want here.
If you want a challenge sewing but a very 2006 look (hey, sometimes being authentic to the time a piece of media was made is good!), a shiny PVC fabric would be a good option. This is again a knit fabric with a plastic (vinyl in this case) coating, but the coating is smooth and has a high gloss. This is not an easy material to sew, however.
If you don’t mind having a less leather-like look but still keeping the sheen, a mid-weight to heavyweight satin would work well.
Almost any of the faux leather or vinyl options would require a non-stick/teflon foot for your sewing machine, which prevents the fabric from sticking as you sew it. I would recommend a stretch needle if you go with any of the knit options, and you may need a heavier needle for certain faux leathers. You may also opt to use a tear-away stabilizer as you sew, to prevent both sticking and skipped stitches.
It’s unclear how her bodice is constructed, and you may want to add boning and bra cups. If this is the case and you end up with a stretch material, make sure that the direction of greatest stretch goes vertically on your torso, and then flatline the material to a non-stretch material to prevent it from stretching while worn. You can also add boning channels and boning directly to a stretch material, and use the advantage of the stretch to cover the complex curves of a bra cup.
I hope this helps! Good luck :]