My suggestion? You're really putting the cart before the horse. Your horse isn't even a horse yet, it is like a newborn foal barely wobbling around the paddock. You should not even be trying to prove anything with this band beyond that you are capable of showing up for practice on time. Even if you write and practice every day, for hours, you probably have maybe two half good songs. That is no slight, that is just a fact.
Two months along is an okay time to start thinking about maybe playing a party, or a new band night at a club. It is hard not to be super eager and want to get the ball rolling, but trying to get opening slots on decent bills before you are ready or capable of drawing, before you have the kinks worked out, could do more harm than good. No one's first shows are any good, but you can avoid being a total train wreck by giving your band time to develop and practice and be a band before you play out.
I've been in maybe a dozen bands over the years that formed just to play a party or a show in three weeks time, wrote five songs in a week and played. That is a valid way to do it, certainly, but the difference is that it sounds like you really want to pursue a serious, music-career minded path and not just be in a Free Kitten rip-off party band like some of us. And if that is the case, you probably want to take a few more months to finesse your songs, sound, performance--like, rather than play the only eight songs you have, play your best eight songs.
If you want to be in a band that is maybe a steady paycheck, I would suggest being a wedding band, or being a cover band, and seeing if you can't scare up a regular weekend night gig at a popular bar. Start a Coldplay tribute band, perhaps. My old bass teacher plays in a blues band that plays in the hallway of United Center during Blackhawks games. My sons' babysitter is in a rad country band that does kids songs and they get hired to play a lot of street fairs and city festivals in the summer. There are ways to make (some) money off being in a regular-gigging local band, but, most of the time, it involves being a jobber and not doing your original music.
So, that said, I think you should move out of your parents house ASAP, get the best crappy job you can and practice at night and on the weekends like everyone else. And then you don't have to give a shit about what they think about you being in a band because you are supporting yourself. When your music is a hobby, it retains its value to you because you need it. Doing music full time is a serious scramble for cash that probably invariably involves saying yes to all manner shit you do not want to do because you have to pay the rent.
The founding of a band is the best-worst time. Have you ever read any rock tell-all where the person doesn't regard that time as the pinnacle of their life? They are always so miserable when they get to the part with the private jet. So, yes, sure, fantasize all you want about your rock star future, but don't forget to be here in this anxious moment, enjoying this awful time with your band. Best of luck, Fan