It depends on your success. Any loyalty hit you take when you jump up a division will be very low, but your loyalty needs to be in the A range to jump to d1, I believe. If you spend a lot of time in D3 though, I think its possible after only a year.
As an example after about 6 seasons in d3, I picked up a C prestige school in d2, had winning, but not great seasons for 3 years, made the nt all 3 years, but never higher than the second round. And after 3 years had only a handful of D- schools listing me as a longshot. After another 20 plus win season and another nt, I had D/D- schools listing me as qualified. My loyalty was A+ both years and my rep was A or A+. I'm sure this would have been faster if I had made a deep run in the nt any of those years. Maybe a general idea for you?