What is the best way to account in Quickbooks for business equipment that will be fully expensed in the year purchased (vs. depreciated over time) using Section 179?

regardless of whether or not you use section 179

A fixed asset is purchased and entered on the books as a fixed asset

then at tax time, if you do elect to use section 179. you do a journal entry for the sections179 depreciation amount

debit depreciation expense
credit fixed asset accumulated depreciation

the fixed asset with a book value of zero ( cost less depreciation) stays on the books until you sell it for scrap or?

If you want your books to be realistic, post normal depreciation based on the useful life, and do not write off the entire cost in the first year, as per Section 179.  You can reconcile book to tax profit in Schedule M-1 of the tax return of this is a corp. or keep a spreadsheet if not