I suppose it will really depend on what type of job you're able to get and the state of the job market where you live.
That being said, I'm not sure you'll be ready to work PRN or per diem after just a month or two on the job. You'll be busy learning how to be a nurse - your foundation skills, time management, delegation, prioritization and all that good stuff - for *at least* the first year or so. If it were me - and it was, just a few years ago - I would concern myself with landing a good first position and learning all I can there before beginning to branch out. Perhaps you might want to get your first job wherever you're going to relocate? The job market is getting so tight that even the magical '1 year' experience is becoming 2-3 years; you might want to give yourself a longer window or move sooner.
The reason people say you need experience - at least a year, if not more - to work per diem or PRN is because you are expected to walk into the role with minimal training and do the job. On my last PD job, I received one night training on a general surg floor before working on my own, (basically: those are the forms we use, I hope you know how to use the computer, there's the supply room and here's a list of phone numbers with your assignment.) Some jobs will offer more training, some even less, but all of them will expect you to have foundation skills in your area and be able to work independently with minimal supervision. That's just not something I see any new grad doing safely or competently, (JMO). PRN/PD rates are higher than regular staff because you will not receive benefits, accrue PTO or have the benefit of guaranteed hours, (you will be first to be floated and cancelled, also), but don't let rates fool you into accepting assignments you aren't ready to handle. It will come in time - it does for all of us.
If you want extra work, depending on what your first job ends up being and the preceptorship you complete, plenty of folks give flu shots, spend a day or two working for a private practice or doing private duty. There is usually something out there to do for extra money, though I don't know any of these areas to pay the rate you're talking about, (most pay much less than acute care, in my experience, particularly if you're a new nurse.)