Are both sentences correct?

Could someone please help? Thanks.

Is Tony picking up the hamburgers, or his brother doing it? – almost correct:

Is Tony picking up the hamburgers, or is his brother doing it? – correct

Is Tony picking up the hamburgers, or his brother picking them? – incorrect

Both of these are correct:

Is Tony picking up the hamburgers, or is his brother picking them up?

Is Tony picking up the hamburgers, or is his brother??

Many thanks, hightor!

Or: Is Tony or his brother picking up the hamburgers?