How do I record Per Diem for meals, received by my company from a client's company, as a nontaxable income item in QBO?

You would create a liability account (in chart of accounts) to put any payments made to go towards the meals and each time your record a receipt for that client for a meal, you would categorize it to that same liability account.  

Example:

$200 deposit received from client in bank feed, applied to liability account

$55 meal receipt received by employee either physical receipt or bank feed transaction categorized to the liability account.   

It is a liability because it is money that you have received but intended purpose has not been spent.  Then you can just run monthly reports in the liability account.