Here is former Fed chair Alan Greenspan’s bullish case for the Gold standard for example [1]
[1] http://www.altavra.com/docs/thirdparty/gold-and-economic-fre...
This is a common myth used to support a gold standard and it's wrong. Barter was rarely practiced because it is too impractical and theoretical. Ledgers and debt existed as soon as imbalanced trade existed.
Paying later is a form of debt. Paying too much is a form of debt. In tribal communities people simply kept the ledger in their head. Some of them used physical objects to remind them of their debts but that is not any different from writing numbers into a notebook.
Common ledgers were tally sticks [0]. You just take a long object and use a knife to mark how much debt you have. They even had a resurgence in medieval Europe because of a shortage of precious metal coins.
Have you read a fair share of other schools of Economics, or did you just focus on Austrian?