Hi, I am working on a project to create an autonomous bird/drone which at random time intervals autonomously flies straight up into the air, hovers for a minute and then returns to ground. What would be a good software for this task? I have not got much experience with drones, how complicated of a task would this be?

Neither Betaflight or INAV have the capabilities you are after. Your best chance would probably be Ardupilot which does have a lot of advanced autonomous flight capabilities, but whether or not it can do exactly what you are after I'm not sure about because I don't personally use or have any experience of it, so I will defer you to the Ardupilot discussion board at the link below where someone on there should be able to answer your questions...

https://discuss.ardupilot.org

I have not used iNav or Ardupilot, but whether or not they can repeatedly liftoff and land a drone reliably might be a question. If your drone has large stable legs and in a flat open field without lots of bumpy terrain/growth then maybe they can do it.
Ardupilot used to accept telemetry commands sent from a PC, it might be possible to have the PC initiate the random takeoff command and land it after the preset time. Otherwise you could add a small MCU/development board onto the drone between the receiver and flight controller to generate the take-off/landing command. That way you can setup the radio to turn on/off the takeoff signal generation, and have an override.

DJI drones have very good self takeoff/landing and there used to be some older models with SDKs that someone with the development know-how could potentially create a macro to do that.