You can divide up the proceeds any way you want. But your reference doesn't address the issue of who pays tax on the capital gain (profit).
You are the legal owner of half the property. The capital gain is yours. If you elect to gift your half to the other person, that does not transfer the tax liability.
I'll go a little further than Critter#2 and say you can't just quit claim your half to her prior to sale. She will need to own your half for two years to claim capital gains exclusion.
