You're going to have to be more specific, because I can only imagine this works if you're only moving from objective to objective, not actually exploring the systems you stop in, which can take months by itself. If you're able to survey a gas giant, you've likely got 10k in expenses, which will add about 30k to a modest trip outside the core.
Both styles can be profitable, but different styles of exploration are done optimally with different fleet configurations. And if you're playing with an eye to economics, then exploring every last corner of every system just in case there's something far off is probably not worth it. Flip on neutrino detector briefly if you have it, but otherwise probably not worth flying off in random directions. Hit the star, hit the planets, maybe make a loop of the ring, and then move on. Also, I don't recommend taking missions where the objective is an unknown location far from the star.
Also, if the gas giant is the target of survey mission, it's presumably paying out 30-80k or for that specific action? So it is worth it in that case. Otherwise, unless it has ruins (i.e. small satellites can be seen in orbit) or it is the last planet in a system you've already decided to settle so you can access the volatiles, there is no economic reason to survey a gas giant. Although a surveying fleet typically has 50-100 supply/machinery reduction, which reduces the costs a fair bit even when you do it, it's still generally not worth the 1,000 credit class I survey data. So again, if you're approaching exploration from an economic perspective, survey the planets that actually do turn a profit.
So for maximum profitability for the objective to objective style (no survey or salvage): Solo Dram (5 crew, 2 supplies/month, 1 fuel/ly)
A 6 month run and 150 fuel burned trip distance: 10*5*6 = 300 credits in salaries, 12 supplies and 100 fuel costs 5,250 credits.
Grab three 30,000-80,000 credit exploration missions on one half of the map and you're profiting 85,000-235,000 credits and getting a peak into systems along the way which lets you do more targeted survey/salvage missions later. Also isn't likely going to actually take 6 months to do that loop. More like 2-3 months depending on mission spread.
Example mid-game salvage and survey everything focus with Bulk Transport skill:
3 Apogees (or Ventures), Salvage Rig, 4 Shepherds, Phaeton
~2340 fuel capacity, ~2610 capacity, over 50% bonus to salvage, 80 reduction in supplies for surveying
73 supplies per month, 14 fuel/ly (167 light year round trip), 540 crew minimum
6 month run, 150 light years, ~128,700 credits running cost over 6 months time
A 50k and an 80k mission to the edge will pay for that which means you break even on the running costs, and then all the supplies and other loot you find along the way (since you're salvaging at a 50% quantity bonus, or 100% if you're going all in and got the salvaging skill), should be pure profit. 2500 units of stuff worth at least 100 credits and above should be at least 250k or so (often vastly more so), plus non-gas giant surveys only cost 5 supplies. Occasionally you luck out and find a drug or weapon stash and come back and sell to a planet in deficit for a million credits.
The Apogees (or Ventures) can handle a fair number of probe defenders without too much worry, so you can use probe country to gather net supplies, fuel, and the occasional gamma core for awhile.
Admittedly, if you are transitioning from a combat fleet to exploration and are already full up on officers, probably will want a commission to help balance out the cost of officers you're not using. Otherwise, skip officers with that fleet setup.
Using my end game combat fleet tends to be inefficient for making a profit exploring, but typically is still enough to profit while doing a circle of bounties and dropping into systems opportunistically to take a quick look around and grab some easy to find exploration loot.