I live about 10 miles from Bush Intercontinental Airport in the Houston Tx area. It looks like I'm dropping out at about 6 or 7 miles from my location. Is this about right for the rinky dink antenna that comes with the SDR?
I think you are using VRS. Go to Tools, Options, Web Server, check "Internet users can see receiver range plots", then on the web page menu, you should have an try "Range Receiver" click that, check "All Altitudes". Now you can click the different altitudes and see what you antenna is doing. You won't see a lot under 9,999', see more at 10,000 to 19,999, etc.
Now click menu, Options, Map tab, Under "Range Circles", check the box next to "Show range circles". Below that you can change the distance, quantity, color of the circles.
All this will give you a good idea of your antennas performance.
There are a lot of options to make what you have better. However HEIGHT get you better no matter what antenna you use.
I started with the stock antenna. 1090 mhz quarter wave is 69 mm. You can cut the stock whip down to 69 mm. That helps some but not much in my experience.
Next I took the bottom off the stock antenna and cut the wire to pull the coax out. I cut the outside sheath back 69 mm, then separated the inner conductor from the outer braid, and made a half wave dipole that I taped outside the glass window. It was only 6 or so feet above the ground but it did amazing for what it was. 40 mile radius on house side 60 mile radius on antenna side.
Like this
https://www.youtube.com/watch?v=ffWmr6p0dho
The I built a quarter wave ground plane (cheap and very easy to build) it is at 8 feet above the ground and I get 80 to 100 mile radius.
My next step is getting it up above the ridge line of the house.
Warning it gets addicting.