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Shareholders' Equity and Share-Based Payments (Details) - USD ($)	3 Months Ended
	Dec. 31, 2022	Dec. 31, 2021	Sep. 30, 2022
Shareholders' Equity and Share-Based Payments
Common stock, shares authorized	75,000,000		75,000,000
Preferred stock, shares authorized	10,000,000		10,000,000
2019 Plan
Shareholders' Equity and Share-Based Payments
Common stock, shares authorized	139,691
Number of shares of common stock reserved for awards	628,825
Share-based compensation expense	$ 283,195	$ 85,609
Unrecognized compensation cost, related to non-vested stock options	$ 0
2019 Plan \| Maximum
Shareholders' Equity and Share-Based Payments
Number of shares of common stock reserved for awards	750,000
2019 Plan \| Employee
Shareholders' Equity and Share-Based Payments
Number of shares of common stock reserved for awards	300,000
Share-based compensation expense	$ 233,125	45,591
2019 Plan \| Non Employee Director
Shareholders' Equity and Share-Based Payments
Share-based compensation expense	$ 50,070	$ 40,018