First about the technical aspects:
The vast majority of 2d game engines are tile-based. That means that the game world is built from a pool of small sub-images of a fixed size. Here is an example. Note that many of the 32x32 tiles in this image are identical to others:
(Image source: http://www.codeproject.com/Articles/106884/Implementing-Auto-tiling-Functionality-in-a-Tile-M)
When your tilesize is 36x36, you could represent your game world with ((360,000 / 36) * (360,000 / 36)) 100 million tiles. The only data you need per tile is the id number of the tile image which is used for it. So when you have between 256 and 65536 different tiles, you will need two bytes per tile, so your world data is less than 200MB. When you have about 1000 different tiles, and each tile is 36 x 36 x 4 bytes, you have about 5 MB of graphic data.
Considering that modern PCs have gigabytes of RAM (assuming that's your target platform), you don't even have a reason yet to not load the whole map into RAM... yet. A good reason to do that will very likely come up in a later development stage.
Now about the gameplay aspects
Assuming that you have a 2d engine with a fixed zoom factor, it's usually not a good idea to have such large maps in a 2d game.
When you have a 3d game, the strong point of a large game world is the ability to present great vistas to the player. Send him to a peak of a mountain, and have him stare at the huge stretches of land beneath him. Then make him realize that everything he sees is playable content, and it blows his mind.
Being able to see into the distance is also a great navigation help. When you see a tower a mile away, you know you just have to keep moving in that direction, and eventually you will reach it.
But that doesn't work in a 2d engine. The player only sees a small window of the game world which is at most 1920x1080 pixels in size on a consumer-grade monitor. He can't make out any landmarks in the distance. That makes large 2d maps a lot harder to navigate. For that reason, large open spaces should be avoided in 2d maps. Every possible map location should have a well-defined set of paths the player can follow and must be recognizable and unique, otherwise it gets too easy for the player to get lost.
As a result from this, the map design in a 2d game must be pretty compact and made with a lot of care about detail. The larger the map, the harder it gets to keep up the quality.