If you put the actual text "1st October" and "2nd October", those are not "dates", they are just plain old text.
If you put the date 10/1/2020 and drag down, you will get consecutive dates. Unfortunately there is no format I am aware of that will display that as "1st October". I am not aware of any format that displays 1 as 1st, 2 as 2nd, etc. There is a format that displays dates as "October 1" if that is close enough for you. With a custom format it can be 1 October, 2 October...
There is probably some algorithm (formula + data in a table) that can convert 1 to 1st, 2 to 2nd, etc but it will have to be done in a separate column. It will not format your list of dates, it would use them as input to the formula.