Bekah, ultimately things like aqadviser are just guidelines and you should stock the tank as you see fit. For me, according to aqadviser, my stocking plan in my 20g is way overstocked but according to experts for Tropical Fish Hobbyist magazine, it's just fine.
I will warn you from experience that panda cories are a little harder than most cories to keep alive. I lost my last one a few weeks ago. :/ They're very sensitive to water chemistry and need soft, acidic water with a pH of about 7.0
Since none of your fish are territorial and all stay small, I think your stocking plan is fine. HOWEVER, since your tank isn't cycled, start with the 6 rasboras first. Unfortunately, both neons and pandas are sensitive to water quality and do best in a cycled tank. :/ So if you can, wait for at least two weeks before adding your 6 neons. Monitor the tank params for another two weeks and then add the cories. Add the ADFS and your betta last and then the shrimp. Once your tank is fully cycled (in about two months), you can even add more neons or rasboras if you want.