I agree with @eandesmom, you should start thinking about the future, where you will live, and start figuring out the real numbers living on your own might mean. For example, you are getting a masters in publicity, so you should be able to figure out roughly what an entry level position with a master’s degree would pay in the field in the areas you might be living in. There are plenty of sites out there with employment data, so it shouldn’t be too hard to get a number, perhaps the median, as a basis for estimating things. As has been said, that salary might appear to be decent, but you have to remember your take home will be a lot lower, as a young person you won’t have a lot of deductions, so will be paying a bit more in taxes.
From there, you can start looking at housing in the area you likely will be looking for a job, and figure out things like how much it will cost to rent an apartment (it is why a lot of young people have roommates, it can be cheaper to share than getting a studio or one bedroom). Factor into that where the job is located, where the potential affordable apartments are, and commuting costs (if any). You might find that your idea of that luxury apartment in the trendy area (if that is what you were thinking of) may not be doable, you might find that a job that seems to pay a lot more may leave you worse off, because to work there and have a reasonable commute, you would be paying a lot more in rent. Sometimes living in a city area can be cheaper than another area, if you live in an area where you don’t have to own a car, that can save you a lot of money.
It will come down to options, and you will have to weigh them. The earlier you do that, the better, it will come up on you fast, and you don’t want to be scrambling after graduation to figure these things out.
Another option might be to live with your family for a while, to allow you some room to figure out where to live, and there is nothing wrong with that. However, if you do that, I strongly recommend at least offering to pay something in rent, to establish that you want to be independent, even if it is nominal, it is establishing that line. If your dad refuses that, then take the money you would be spending on rent at home, and save it, so you won’t be tempted to spend it. That money when you decide to move out can be used for a security deposit, moving costs, getting stuff for the apartment, etc. And again, it is to get you into the mindset that you will be supporting yourself.
Whenever you decide to move out on your own, your dad may try to be heavily involved in the process, but I strongly recommend you keep him out of it. From the description of your dad, he is really generous, which is great, but he might be strongly tempted, for example, to have you get an apartment that is way too upscale for what you could reasonable afford on your own, for example, insisting you get your own place rather than consider sharing an apartment, or in a more upscale area. Dad’s are protective, especially with daughters, and I am sure he would want you to have ‘the very best’, but that would just reinforce your dependency on him. If he does want to help financially, then I would strongly encourage finding an apartment that you would barely be able to afford, and for a given time he helps with the rent, so you wouldn’t be struggling. If he does this, it should be for a period of time (maybe a year), to allow you to get your feet, and hopefully be making enough after a year to be able to afford it on your own.
Speaking only for myself as a parent, the thing that most makes me proud of my son is that he has consistently made more and more of his own decisions, and while he is financially dependent on us, will be for a while, he has always tried to minimize that dependence on us, is grateful for what we gave us but often is in the position of telling us no with things we offer to do for him. I think showing that you want to step out on your own, on your own two feet, will in the end make him as proud of you as anything:)