I suggest for sole proprietors and partnerships the owner/partner equity accounts look like this (one set per partner):
[name] Equity (do not post to this account it is a summing account)
>> Equity ( first of the year roll up drawing and investment into this account as well as retained earnings)
>> Equity Drawing (record the value you take from the business here)
>> Equity Investment (record the value you put into the business here)
The way you mention for debiting the expense and crediting equity investment will work. But QB can be funny with journal entries, sometimes they do not show on reports.
I prefer creating a cash type bank account called partners
use write checks, do not print this is data entry, to record the payment of the expense, and in the memo block enter the partner name.
when all expenses are entered for partner one, total them and make a deposit using partner [name] equity investment as the source account for the deposit
then do another partner