Compare ögonblick to Augenblick for you German learners out there!
I never use it that was personally, but according to Wiktionary, yes.
As far as I know, på and om are not generally interchangeable as expressions of time. på + time span means something requiring that length of time; om + time span means something will happen in the future within that time. I find translations for both "om ett ögonblick" (in a moment) and "på ett ögonblick" (instantly). It seems på emphasizes the brief period of time involved, while om is a more vague expression that could be on the order of minutes, which I think is what's wanted in this sentence (in English, "in a moment" is often stalling for time without giving a specific estimate).
Also, på has many other uses in time expressions (time of day, days of the week, seasons), but I've only encountered this one for om.
That's my analysis, but perhaps a native Swedish speaker can weigh in with a better explanation :)