It depends on the diameter of the trap. Under International Building Code use table 906.1.
A 1.5" trap can be 6 feet from the vent (if your trap is only 1.25" the maximum distance is 5 feet).
It looks like you should be fine in your situation.
Two options. Air is going in, or air is coming out.
"Gurgle" is caused by air being forced through the water in a fixture's trap. It's similar to the "glug" generated when you pour milk quickly from the milk jug. It's air being forced through liquid, in an attempt to equalize pressures.
Air in
Vents placed strategically throughout the plumbing system, typically provide an adequate amount of air. If the vent(s) get clogged/blocked/restricted, pressure differences inside and outside the system will develop. If these differences in pressure are large enough, air will be forced through fixture traps in an attempt to equalize the pressure.
In this case, clearing vents; or adding additional vents in the case of improper venting, will usually resolve the issue.
Air out
If a large enough object (liquid and solid waste) is moved through the system fast enough; in such a way that the object blocks the entire internal pipe diameter, a high pressure zone can be generated on the front side of the object. This high pressure zone may be able to force air out through fixture traps, as the object travels through the system. Think of it like the plunger of a pop gun.
In this case the solution is to increase the diameter of the pipe, eat less fiber, use less toilet tissue, or decrease the flush power of the toilet.
Best Answer
It's not going to be easy, but it's possible. The toilet drain pipe is going to be 3", and won't have a trap (since the trap is built into the toilet). The toilet will also only have a cold water supply. The tub drain pipe will likely be 1 1/2", and will have a trap. The tub will obviously have both cold and hot water supplies.
To switch the location of the fixtures, you'll have to reroute the plumbing for each to the new locations. Depending on the current location of the fixtures, existing plumbing, and the amount of access to the plumbing. This job could range anywhere from not so bad, to a complete gut and rebuild.