good point by oldfishlady...
regardless of what size tank you bring into the equation....you have two different kinds of fish which requrie two really different types of water parameters...as pointed out, you're lookin at a temp difference of almost 20+ degrees!! Thats alot for some fish to cope with. if you are going for a bigger tank, you'll need to keep in mind most Goldfish
will need anywhere from 40-75 gallons a piece
when fully grown.
You should also up your Neon Tetra
count to atleast 6, they are shoaling fish which enjoy being in groups of 6 or more to ease their stress level and keep them comfortable.
What kind of plant is it? You said their stems are very small...a pic of type of plant would be most helpful.
One side note...you said you have an air bubbler(wand)....most planted tanks are recommended not to have anything breaking the surface of the water, when that happens your tank loses oxygen, which your plants need to live.
jsut some things to think about....pic or type of plant would help us out!