It not clearly mentioned anywhere that how Doraemon earns money. But by watching Episodes of Doraemon we can come to conclusions of earning resources.
1. Owner of Doraemon (Nobita's great-great-grandson - Sewashi) is funding Doraemon.
The reason for which Doraemon came from future is that to improve the academic performance of Nobita. Because of this reason Nobita's great-great-grandson was getting very less pocket money. If Nobita's great-great-grandson was rich then he did not required to have send Doraemon back into the past to Nobita. That means Nobita's great-great-grandson would have not been funding much to
Doraemon. That cut out this funding possibility.
2. Through money making gadgets.
Doraemon possesses quite a few money making gadgets like rice cake maker, time cloth, multiplying bank and so on. Since he is from the future, he knows how to use these gadgets to support himself. Also, he has the ‘Devil’s Passport’ which is the ‘Ultimate Credit Card’ as you can use it to get anything for free, absolutely.
But sometimes Doraemon also runs out of money as these gadgets does not provide a lot of money, as if they did Sewashi (Nobita's great-great-grandson) would have not send Doraemon on the first place.
So, I think point number 2 is the answer to your question.
Note : Name of characters has been referred from this link https://en.wikipedia.org/wiki/List_of_Doraemon_characters