I find I often need a word such as this. Some people are just relentless querulants and I want to be able to refer to that aspect of them, e.g. "John's relentless querulism". Doesn't seem like that's a real word though...
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FumbleFingers is right in saying that querulant is not in the OED, but querulist, 'A person who complains, a complainer', is. The corresponding noun, also in the OED, is querulousness, meaning ‘The state or condition of being querulous’ and it's probably the word you're looking for. However, you may want to be sure your intended readers will know what these words mean before using them.
As Barrie says, querulousness (or querulation) are the actual derived terms.
But in practice most people would speak of John's constant carping.