I dont know your govt, what it provides, in nz we had a sickness benefit, and an invalids benefit. The sickness benefit got scrapped and it all got lumped into a jobseekers benefit, but it wss just renamed, it was basically the same. I think the govt just did not want people abusing it and faking illness to get out of work. The invalids benefit, as far as I know, was for permanent conditions.
While the sickness benefit meant if you recovered you could go back to work if your doctor gave you the all clear. you had to check in with your doctor every 3 months or so so they could advise you. My advice is to have a chat with your doctor about it. And also think about the kind of work you could do, whether part time, causal or full time, what you are ready for. It might be, you focus on recovery and do voluntary work for a while, and then you not under pressure or stress with work commitments while your body gets strong again.
In the meantime even if you dont have any income coming in, do not worry, God will provide all your needs.
It seems to me your dad is worrying over the stigma of having a son on the benefit, maybe, but it just depends on you and your doctor and you agreeing what you are fit and capable of. Some people just want to stay on the benefit and fritter it away because they have labelled themselves invalid but I think theres all kinds of work people can do if they put their mind to it.