aside from any possible quarantine issues with your dog, i don’t know if anyone would want to hire a person for so short a time, but don’t be dissuaded from trying. iceland has a very low unemployment rate, about 1-1.5%, so as a whole, iceland needs workers. most jobs require icelandic, of course, but some don’t, like some health care, restaurant work, or even highly skilled IT work. when i was there i met Polish immigrant restaurant workers whose icelandic was almost nonexistent. i would also think that there must also be seasonal work you can do. if i had only two months i’d even go wash dishes for pocket money for an adventure. you could easily meet people who could help you out later on…

Here is a link of all the vaccinations required and the length of quarantine for a dog to be imported to Iceland.
http://www.lbs.is/Uploads/document/eydubl_ensk/leidbein_hd_kt_enska.pdf

If you don’t speak Icelandic, finding a job can be difficult, but contact your embassy there and they may be able to help you.

About accommodation, nothing is cheap in Iceland, because it´s one of the most expensive countries in the world. Despite all the negative things I´ve said, I really recommend you to visit Iceland. It´s certainly an interesting and quite different country.

About your questions, why not contact an Icelandic embassy or consulate, or perhaps a tourist agency arranging travels to Iceland can help you!

Good luck, I really hope you get to visit Iceland (and your dog too)!

Reykjavik is the country’s only city but Akureyri and Egilsstadir are also very lovely towns.

The best thing about being a tourist in the island is how realtively small it is. You are never more than a few hour drive from any tourist attraction or landmark you would like to see.

I recommend you check out the summer night-life in Reykjavik and also a fair number of Iceland’s most favorite landmarks. A few of them would be the Blue Lagoon, Gullfoss, Geysir, Godafoss, Seljalandsfoss, Barnafoss, Skogafoss, Svartifoss, Dettifoss, Dynjandi, Seljavallalaug, Lake Myvatn, Thingvellir and the Westmann Islands.
-Note that all the places ending in ‘foss’ are waterfalls.

Reykjavik is really the only City, and not even that is a City on a US scale. The total population of Iceland is 300.000 and the greater Reykajvik area has about 150.000. Apart from Reykjavik you have smaller towns and a lot of nature, which by the way is void of trees for the most parts.