I'm an auditor -- so this is the auditor in me coming out
Using a 0% interest rate (for one year) cc for miscellaneous expenses is OK. But I'd advise when you get your $10K adoption tax credit that you pay off any balance on the cc first. Since your interest on the equity loan is tax deductible -- and interest on the cc isn't. Also any cc that gives you 0% rate for a year usually has a pretty high interest rate after the year has elasped.
Best wishes!