I have an LLC with two members
No you have a partnership, registered with the state and with its own EIN from the IRS. LLC is just a state registration concerning company liability.
One member has made a contribution this year in the form of furnishings for a rental unit. I would like to track the cost as an owner contribution and an expense for the business, but would also like to track the furnishings as a fixed asset for the rental unit so that I can track depreciation.
Well you can't have it both ways, it is partner equity investment and a fixed asset. Whether you expense the fixed asset at tax time using section 179 accelerated depreciation is tax time decision.
Open the register for the partner equity investment account from the chart of accounts, make a new entry as an increase and use the fixed asset account you create first as the account. The contribution is at fair market value, defined as the price a buyer would pay for it and the seller would accept.
Journal entries should be the exception when using QB, they often do not work as you think they should, and when you use inventory type items they never work for inventory. It is much better to use the forms on the home page the way QB is designed to be used. Journal entries also bypass accrual/cash reporting, and will not show on many reports.