I’d just keep going and see what happens. it’s working right now, you’ve got the bug to run again (that’s good right?), keep doing what feels right and adjust as you go.
depending on your long term fitness/performance goals, you may find (later) that you can’t get there if you’re not fueling for them. healthy carbs & proteins will become more critical for the runs themselves and for recovery, strength, mind & mood, and preparation for your next run.
don’t skimp on the hydration either way. omad notwithstanding, you may find your electrolytes need replenishing during and after a run and that’s about survival.
that distance, its not going to make a blind bit of difference. You should be able to do an hour run (or other moderate exercise to work up to it) without worrying about stuff like this.
There is a lot of pearl clutching online about eating, nutrition, blood sugar etc….ignore it. Unless you are at very very serious/pro athlete level, it does not need to be a concern.
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Try it, see how you feel, but its going to be personal preference only.
I do omad and run in the morning, eat at night. Unless I’m running more than 10 miles that day I stick to omad. If it creeps up towards half marathon I may eat something at lunch depending on how I feel. If I do eat usually just protein and fat too see me through to dinner.Most days are just 3 to 6 mile runs though and no problem with not eating until dinner, water and black coffee see me through