The wood looks like untreated pine so that looks OK. As long as the wire is not galvanized, while not ideal it should be OK for a short while. Would recommend getting a more suitable cage in the future.
I, a self-avowed Queen of Paranoia, confess to similar worries...
I don't mean to be critical: I just know how you must treasure that little angel, so I, too, would hope for a standardized cage UNLESS you are very confident about your materials and construction skills, which maybe you are.
What a darling!!!!!!!!!!!!!!