You may find your span stretches a bit anyway, over time. I took up playing piano seriously again a bit less than 2 years ago, after about a twenty year gap. At that time, I could stretch only an octave, and it was quite difficult to play a lot of octave runs in a piece. Now less than two years later I can stretch a ninth, and the octave runs are reasonably comfortable. I have been deliberately working on this, playing scales in octaves, and keeping going with some pieces which I find quite a stretch. Chopin etude 10/3 I've found quite helpful at stretching my hands, even though it's sixths rather than octaves - the sixths are played not only with thumb and fifth fingers, but also with second and fifth fingers, or thumb and third fingers and doing those stretches seems to have helped my octave span too. This is probably not a piece for someone who has only been playing for a year, but the principle could be applied to develop an exercise in sixths.
I was pretty much shamed into doing this by my teacher, who is a typically small Chinese woman with tiny hands, who can nevertheless play wider spans than I'm comfortable with!
Kathryn