Congratulations with your choice. I've been playing bass for 10 years now and it's a great instrument. I see myself as a true bassplayer although lately I've been working on my guitarplaying as well (for me a better instrument to compose).
Frankly, if you have been playing for just four months, I don't think you should consider upgrading yet.
This may not be true for you but when I was in your phase I too was already looking around for a better and more expensive instrument, assuming it would play easier than
my Yamaha Attitude Standard (comparable pricerange as you P- bass) which was my first bass.
But it's all in the fingers, my friend!
A Squier P-bass is a fine instrument and when you develope your bass playing skills you will be able to let it kick butt. You don't need a $1000 bass for that.
Yeah, eventually I replaced my Yamaha. But that was mainly because I made it fretless and I wanted a 5-string. Now I sometimes miss it as it was because it was a really fine bass.
But there is nothing wrong with a bit of dreaming of course. And in case you might be wondering: I now have a
Ibanez ATK-305. Great instrument, just not for people with small hands and a weak back.