Connecting in Dubai on different airlines

At DXB Quantas departs from T3, and Air India arrives at T1, so you'd have to transfer between terminals. AFAIR there is airside transfer at DXB, so if you have no luggage, and check in online/come to a staffed transfer desk, you could proceed directly. If you have luggage, you'd have to re-checkin and go through immigration; there is a free shuttle between terminals. As a US citizen you don't need a visa. Immigration at DXB is usually fast, and with 6 hours layover you'll even have time to briefly visit the city if you want to.

You don't need to collect your bags. Just walk upto any dnata transit service desk and show them your tags. They will collect and re-check your bags; assuming you have boarding passes for your next trip.

If you do not have boarding passes, you will have to enter the country. As a US citizen, you can use the e-gate and don't need a visa. Simply go through the e-gate procedure, immediately after the e-gate is a security check point for hand luggage and after that there are the luggage carousels.

Collect your bags from T1 and then take the free shuttle to T3; or (depending on how much luggage you have) you can take the Red line metro.

At T3, you need to check-in for your next flight, go again through immigration and security controls and then you'll be in the vast transit area of terminal 3.

Note that depending on your flight - you may have to take the train to the F gates (which are for the A380). This adds about 15 minutes to your total foot journey time.

If traveling with minimal luggage, then entire process is easily finished in under 2 hours (counting for queues at immigration, the various lifts you have to go through, collecting and waiting for your bags, waiting for the queue for the shuttle, and check-in).

Rushed, you can do it in 1 hour but you'll be exhausted by the time you check-in again - there is a lot of running around you have to do. Especially in T3