Your pH is certainly on the basic side. The dGH isn't a problem since many fish occur in that range. The trick will be combining those two things along with a 10 gallon tank.
The small tank size means we should eliminate things like rosy barbs (6.0-8.0, 5-20 dGH), cherry barbs (6.0-8.0, 2-20 dGH), Odessa barbs (6.5-8.5, 5-20 dGH), gold barbs (6.0-8.0, 2-20 dGH), pearl danios (6.0-8.0, 1-20 dGH), zebra danios (6.0-8.0, 5 -20 dGH), blind cave tetras (6.5-8.0, 5-25 dGH), black widow tetras (6.0-8.0 but preferable lower than 7.0, 5-20 dGH), white cloud (6.0-8.5, 5-20 dGH), silvertip tetras (6.0-8.0, 5-20 dGH), pristella tetras (6.0-8.0, 2-20 dGH), glassfish (6.5-8.0, 8-20 dGH), emerald Brochis (5.0-8.0, 2-15 dGH), bronze cories (6.0-8.0, 2-15 dGH), rainbowfish (too lazy to list them all), Inle loaches (7.0-8.0, 12-20 dGH), forktail blue eyes (7.0-8.0, 15-30 dGH), Asian rummynoses (small but combative 7.0-8.0, 10-20 dGH), most livebearers (again too lazy and you know the ones easily found already), ok I think that's enough there and hardly exhaustive since I did it off the top of my head.
So what would I suggest for a 10 gallon with your parameters? Guppies Endler's Rosy Loaches
(you'll see 24" suggested, I'd feel better about putting a slightly more than 1" fish in a 10 than anything in the above paragraph though) Emerald Rasbora
(Seriously Fish differs in the pH range from here listing up to 8.0) Scarlet Badis Red Dwarf Rasboras
More to come when I can get the internet to behave and if you want.