My first visit to Croatia was in early October. The weather varies year to year of course - but while I was there, the weather turned from warm and sunny to cold and rainy. It was warm (and busy) in Dubrovnik while I was there, but the rain came by the time I got to my next stop Korcula, which in early October seemed dead and about to close up for the season (restaurants were open at night but you had to walk up to them to see, it didn't look like they were). Granted this was 2009, and I think tourism has increased a bit since then. But I usually don't enjoy visiting a place where people aren't out and about and I am one of the only people eating in a restaurant.
But if you are interested in excursions, note that the beginning of October in Croatia seems to mean reduced options - shorter hours, fewer ferries, etc. On the upside, maybe fewer tourists. And although the weather could be perfect (or it could be rainy in September), the odds of poorer weather increase as you get into October.
If I were going to Croatia again in the fall, I'd aim for the last two weeks of September myself.