First of all, HOW HARD DO YOU WANT IT TO BE?!? Do YOU WANT them to get to the city? (It appears not, or you would have given them Chocoboos, or
something!) If that's the case, then just tell them that, without axes, it will be too hard to cut down the trees... best to start walking! (Then you can deal with some Dwarf with Stonecunning telling you that he crafts a stone axe!)
If you don't really care, I'd tell them that they can rig up a raft that should survive the trip (no whitewater) in about a day, if they plan it, select the wood, all work together to cut the logs and float them downstream to where the raft will be assembled, and then tie them together with some rope... Building a raft really isn't all that hard (and how many people carrying what makes them 2,500#?!?)
Now make some tasks. I'd say to design a simple raft is DC:10 Knowledge (Engineering), DC:15 if they want a tiller. A successful plan adds a +2 Sybergy Bonus to building the raft. Every person gets to make an unskilled DC:10 Craft (Shipbuilding) or DC:15 Survival task, with each success adding another +2. Once all of the logs are assembled, five are laid parallel over two or three at right angles, and then everything must be tied down with DC:15 rope use. This latter step can be redone, if failed. Just untie the rope, and start again. Since there's no danger of combat, a few ranks of skill and "Take 10" should suffice (+2 for silk rope). The whole thing should waste a day, or so, with tools (more without).
Once a raft is built, navigation is as easy as following the river. They pole along until they get to where they're going (unless the river forks). Getting lost is covered in the DMG, and is generally handled by the Survival skill.
How long it takes depends upon how far the town is, how hard they pole, and the speed of the current. In other words, it takes as long as you tell them that it does... Duh!