Is it safe to drive between these cities at night?

No. Avoid night driving due to poor road lighting and wandering livestock.

Should I fly or drive?

Drive. The circuit is about the landscape, which you miss entirely if you fly between cities.

How to plan a Rajasthan desert circuit beyond Jaipur

Skip the Jaipur-only route by taking a train or hiring a driver to reach Jodhpur and Jaisalmer, where the desert landscapes truly begin. Allocate at least 7 days to cover the vast distances between cities and prioritize time in the Thar Desert over urban sightseeing.

Choose your transport strategy. Hire a private car and driver for the duration of your circuit (roughly $50–$60 USD/day). It is the only way to make spontaneous stops between cities. Alternatively, use the overnight trains between Jaipur and Jodhpur to save daylight hours.
Map your route by distance. Do not attempt to drive more than 6 hours in a single day. Route: Jaipur to Jodhpur (6 hours), Jodhpur to Jaisalmer (5 hours), Jaisalmer to Bikaner (5.5 hours), then back to Jaipur (7 hours).
Book desert camps early. If visiting the Sam Sand Dunes near Jaisalmer, book a tented camp at least 4 weeks in advance. Avoid 'tourist trap' campsites near the main road; aim for camps 20km deeper into the dunes for a quieter experience.
Sync with the climate. Only visit between November and February. Temperatures in the Thar Desert plummet to 5°C at night and reach 30°C during the day. Avoid March to June unless you want to experience extreme heat.

Is it safe to drive between these cities at night?: No. Avoid night driving due to poor road lighting and wandering livestock.
Should I fly or drive?: Drive. The circuit is about the landscape, which you miss entirely if you fly between cities.