Hello and welcome!
Looks like you have a nice bike and you are off to a great start! You can certainly achieve your goals if you set your mind to it.
Getting better... hhhuuummm... you are still very new... and others have given good advice.
Hill training is always good. It's also nice to have a mix of rides in your schedule. Short days, long days, faster days, slower days, etc.
I think my advice to you though, would be this... get a computer with cadence on it and know how to use your cadence reading.
It wasn't until I got a computer with cadence did I really figure out how/when to change the gears. When I learned that... my speed and overall average improved.
The key is to try to maintain a 90-95 cadence. Finding a perfect balance between using your power efficiently and not giving it away. If you have too high of a cadence, then you are just giving away your power.
Now... keep in mind that when going up a hill, unless you have a granny gear (triple) you probably won't come close to that cadence, but try to get as high of a cadence that you can.
Good luck!
"Life is not a journey to the grave with the intention of arriving safely in a pretty and well preserved body, but rather, to skid in broadside thoroughly used-up, totally worn out, and loudly proclaiming: WOW WHAT A RIDE!!!!"