Stock-Based Compensation - Expense (Details) - USD ($)	3 Months Ended		6 Months Ended
	Mar. 31, 2020	Mar. 31, 2019	Mar. 31, 2020	Mar. 31, 2019
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Stock-based compensation expense	$ 304,539	$ 267,742	$ 664,016	$ 1,140,031
Accrued directors' fees settled in fully vested stock options			49,121	49,121
Research and development
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Stock-based compensation expense	41,148	120,763	148,938	211,972
General and administrative
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Stock-based compensation expense	$ 263,391	$ 146,979	$ 515,078	$ 928,059