Shouldn't be any problem.
If I was in your position, I would brew, cool, and rack to the bucket/carboy. Immediately start brewing again (if it's extract...if you're doing all grain, you should be mashing one batch while cooling the other, if possible). Roughly split the brew time in half to determine when to pitch yeast (if the second batch will be ready 3 hours after the first, pitch yeast after an hour and a half).
That would leave little to worry about in terms of infection. And oxidation would not be a concern.
P.S. Oxygen will not hurt yeast at all...they love it. It will ruin a batch of beer after fermentation really takes off, though. Oxygen before or immediately after pitching yeast is good; oxygen well after yeast is pitched is bad.