And if not; why did this specific type of boat only develop in one city? Why not in other cities with canals such as Amsterdam?
Gondolas are a unique design of boat in that they are asymmetric.
The port side of the Gondola is longer than the starboard side. This compensates for the fact that the Gondola oar is on the starboard side, and the stroke of the oar would cause the Gondola to keep turning to port if the hull were not asymmetric.
(A single paddler in a canoe, for example, needs to use a "J-stroke" to keep the canoe heading straight, because the canoe hull is symmetric, and would turn away from the side on which the paddle is deployed if the "J-stroke (which keeps the canoe straight, but dissipates energy) were not employed.)
(The punt uses a punt pole, which pushes against the river bed, not against the water like an oar or a paddle. The punts-man needs to use a technique somewhat similar to a "J-stroke" to keep the punt heading straight when poling over one side.)
(The use of two oars, as in the typical rowing boat, is fairly efficient, but the standing gondolier faces forward (so he can see where he is going better) and pushing forward on his single oar can put more weight and power into the stroke than a seated oarsman (unless the oarsman has a moving seat - like a racing scull - so he can add the thrust of his legs to that of his arms and back), A moving seat takes up a great deal of room in the boat, which cannot be used for passengers or cargo, and the oarsman is still facing backwards and cannot easily see where he is going.)
The gondola is very efficient in its use of a single man power on a single oar due to the hull form.
The gondola has evolved over time, and reached its current form only in the 19th century, as developed by the Tramortin boatyard.
http://en.wikipedia.org/wiki/Gondola
Earlier gondolas generally had two rowers and did not have the asymmetric hull.
Gondolas are complicated and expensive to build, but they are the fastest and most efficient passenger or cargo carrying (thus eliminating single racing sculls) one-man-powered boats ever built.
I suspect that the main reason why the Gondola design did not spread beyond Venice is that it was not perfected until the 19th century, and about the time that it was perfected, steam engines and mechanical means of propulsion began replacing man-power on small boats around the world.
Another reason is that the Gondola needs certain economic and geographic conditions in order to thrive as a boat design.
The Gondola is an expensive boat to build. For it to be used, the operational cost saving (of having a one man crew rather than two or more) and the value of efficiency (able to carry passengers or cargo faster than less expensive one-man boats) both need to be enough to offset the higher cost of the boat.
The Gondola is an excellent design for calm to choppy waters (like the Venetian lagoon) but not such a good design for the open sea (the flat bottom, and especially the exposed position of the oarsman, standing on the stern deck, make the Gondola less suitable for rough waters than say a Grand Banks fishing dory).
[Punts](http://en.wikipedia.org/wiki/Punt_(boat)) are pretty similar and were used in Cambridge and Oxford; but the Gondola is specifically from Venice.
The difference between Amsterdam and Venice is that Amsterdam has canals on land, whereas Venice is itself built on water, small streaks of land, and small beaches. The 'Lido' in Venice (an outer island) was just a plain beach back in the 1500s (lido is the Venetian word for beach). Amsterdam has a lot more roads, avenues, and places to walk. Bridges and Gondolas were necessary in Venice -- if a bridge in one area broke, a Gondola was possibly the only means of moving around the city (conversely, there aren't too many places in Amsterdam where you could get stranded).
So, Gondolas are Venetian; similar boats existed in England; and Venice is so peculiar among cities of the world that such a water-taxi-centric means of communication never was used extensively outside La Serenissima.