I got a job offer after a phone interview (need advice)

So this job is in South Carolina and I am in New York. I do graphic design. It is at a 2 year old marketing company. I have no idea what to do or if its a good idea. I am at a good job but its part time and I have been working there for almost a year and I am not sure if it will go full time at this point. The company down south said i could work remotely for a few weeks.

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I want to move because its just way too competitive here for graphic design and money goes a long way down south.

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Is it normal to get an offer after a phone interview? They did not even ask for references.

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