Yes, female plug on the inverter OUT circuit is fine.
Had to read it twice to verify that you were not considering a "dead man's plug" which is a male plug on a powered/hot circuit.
And, if this is an expensive inverter, may be cheaper to just buy a 30 amp ATS to replace the built in ATS in the inverter OR repair/replace the ATS in the inverter.
Several options here depending on quality/cost of current inverter.