Two best practices of Scrum are :
Grouping your staff in small teams.
Keeping communication quick and efficient (especially meetings).
So yeah, definitely, Scrum fit a small organization. In fact, as a small organization, you need less REorganization to start applying scrum !
Yes, but...
A problem I've encountered with Scrum in a small organization, is that the Product Owner was frequently unavailable (due to having lots of other responsibilities as well).
Needless to say, this can severely affect your agility. If you want to apply Scrum in such a situation, be sure to clearly communicate that the role of Product Owner is a time-consuming one.
Scrum is best suited for a small organization because of the following reasons:
I guess these are enough reasons. Take it up in your organization.
Just make sure to have someone who knows the process well to implement it for you. Also, good to get a coach for the first Sprint.