We are currently looking at an itinerary that would take us to Dubrovnik the 13-15th of October. Is that getting too late for optimal weather? We could postpone this trip to September of 2020.
As a matter of fact, the best time to visit Dubrovnik is September and October. Most of the cruise ships are gone by then and you have the whole town for yourself...the locals of course, and few tourists like you. The weather is not that hot and dry, and prices may be lower too, once the season is over. As long as it doesn't rain, you have made a great choice! Have fun!
I traveled through the Balkans during September and the first half of October 2015. Weather in Bulgaria began to change in late September, becoming rainier though still pleasantly warm. Raininess continued in Montenegro in early October and in Zagreb the second week of October. It definitely was no longer summer in Zagreb. The transition to fall culminated on my last full day in Zagreb (I think October 10), when it was quite chilly and rained cats and dogs all day.
That was just one year and is not predictive, and Dubrovnik is probably both warmer and less rainy than Zagreb, but there's a website you can use to take a look at actual day-by-day weather in recent years. I suggest that you go to timeanddate.com and see what it has for Dubrovnik in mid-October of the last five years. I've linked to data for October 2018, which seems to have been a very nice time to be in Dubrovnik.
I visited Dubrovnik for the first time in mid-October. It was still warm and sunny all three days. I was glad I had my shorts to wear when walking the walls one day! The day I left, however (for Korcula), the weather changed dramatically - a storm came in and the temperature dropped dramatically, and I had a mix of sunshine and occasional heavy rain for my last four days in Croatia. Someone whom I had met in Dubrovnik and stayed after I left told me the Buza Bar closed for the season the day I after I left because of the weather change.
So yeah, you are taking a bigger chance the later into the season you go. You're playing the odds. You could get the beautiful warm weather I had the days I was there or the cooler, stormy weather they had the day after I left.
I don't think I'd postpone my trip til 2020, personally, just for that. You do get the benefit of probably fewer tourists in October than September - and who knows, it could rain then too.