No, that gap isn't too large. When your distances become greater, you may need train at lower intensity since you wouldn't have a whole lot of recovery time between sessions.
I'm starting week 2 on Sunday. I run Sunday, Tuesday and Thursday and do other workouts in between. I started this to prep for a 5k on March 13 this year and could always use the extra motivation!
I started with C25K last January, on my 59th birthday. I'll be running a 10 K this January on my 60th birthday. My only goal is to finish the race! Running has made me stronger in every imaginable way.