Back up here, you're jumping too far and too fast on this pH.
First, pH is related to the hardness, primarily the carbonate hardness (KH, or Alkalinity). Attempts to adjust the pH will fail if the KH is high enough to buffer the pH. So I don't go repeating everything, you can read how this works here: http://www.tropicalfishkeeping.com/f...quarium-73276/
Trying to adjust the pH when it is being naturally buffered will result in fluctuating pH, and if you should happen to pass the buffering capacity, the pH will very suddenly crash (drop) and this could kill the fish outright. The fluctuating pH stresses them considerably which weakens the immune system and this can lead to an early demise too.
The other point is the fish. There is no value in raising pH to 7 or higher for soft water fish that do best in (obviously) soft slightly acidic water. We can discuss this more when we know numbers for GH, KH and pH of the source (tap) water. You can test the pH (let the water sit overnight before testing), and get the GH and KH/Alkalinity from the water supply folks, they may even have a website.
On the cycling, what was mentioned previously is true. However, fish that live in very soft acidic water in nature, can do the same in the aquarium too, with no ammonia or nitrite issues. In acidic water ammonia automatically changes into ammonium which is basically harmless. The bacteria will still function though more slowly. Here's more info on this: http://www.tropicalfishkeeping.com/f...quarium-74891/
Another issue here is the neon tetra. This species is a shoaling fish that needs company; it will be highly stressed alone, and probably waste away. But there is insufficient space in a 1-2 gallon tank for this or any other tetra. This is a whole other problem which I will leave for the present, but I just wanted to caution you on this fish. But we do have fish profiles, second tab from the left in the blue bar across the top; if a name is used the same in posts, it will shade as it did here and you can click on that for the profile. Each profile includes data on numbers, minimum tank size, water parameters, etc.
Last, but certainly not least, welcome to Tropical Fish Keeping forum.