Michelle Mellotte, 61, took the money from Michael McGrory in February 2010, saying it would be repaid that summer.
But it was only returned after police began an investigation the next year.
The former doctor in Ederney now faces being struck off the medical register.
The judge told her there was little the courts could do to punish her more than the public humiliation of exposing the "significant breach of trust".
She admitted fraud by abuse of her role.
The judge told her the offence warranted a 12 month custodial sentence, but it would be suspended for two years given the exceptional circumstances of the case.
The court, sitting in Downpatrick, was told that the victim, Michael McGrory, was suffering from Alzheimer's and the GP was aware of his deteriorating mental and physical health when she asked him for the loan.
She went to his home to "ask him for a favour" to help her out of her financial difficulties and he agreed to sign a cheque for £10,000 in the presence of his home help with an endorsement that it would be paid back in the summer of 2010.
The home help confronted the GP a year later when the money was not repaid, but she told her "not to worry about it".
The money was returned to Mr McGrory, who died in 2012, after the police began to investigate the doctor's conduct.
The judge said the GP was not motivated by greed and the money was not spent on a lavish lifestyle, but was rather a result of her financial mismanagement.
He said he had received many testimonials and it was clear Dr Mellotte was dedicated to her patients, and had cared for many people in a compassionate and selfless way.
He said she not only looked after their medical needs but also helped their housing and financial needs, giving people money who were in arrears for rent, and regularly buying groceries for patients.
The judge said the GP did not see anything wrong with this approach, which he described as not only "unorthodox but inappropriate".
He said she was dedicated to her patients but was less interested in the financial aspects of her practice, and described her practical financial management as "inept".
The court was told that the doctor suffered from a history of depressive illness and was in significant financial difficulty and pressure from her bank at the time.
The judge said the offence did not start out as one of dishonesty and the money was used to repay other individuals, including another patient she owed money to.
He said that Dr Mellotte had cared for many people in a compassionate and selfless way for four decades but her career had come to an end in a "publicly inauspicious way".
He said this was a "significant punishment in its own right" and that it was right that the significant breach of trust in the doctor-patient relationship had been publicly exposed in this way.
A Fermanagh GP who dishonestly exploited and took advantage of a vulnerable elderly patient when she failed to repay a £10,000 loan has been given a suspended prison sentence.