Doctors working on Dutch slave ships had a relatively high mortality compared to the rest of the crew. This is supposedly due to their contact with the slaves: they were required to examine any slaves offered for sale on the African coast. Examining all slaves on board two times a day was also part of their duties. This included checking their mouth for signs of disease. So yes, there are known cases of doctors dying due to patient contact.

If I may ask a related question: Was it common for Doctors to pass on diseases or infection from patient to patient?

Lets address your question first. Not all epidemic diseases are caused by bacteria, viruses can cause diseases too. Antibiotics would do nothing in the case of a smallpox or ebola outbreak.

While I haven't been able to find direct statistics or records to show that doctors had a higher mortality rate compared to the general population. However, I am aware of several examples of doctors who treated epidemic diseases. It may be a partial answer to your question, sort of.

The pathogenicity and the contagiousness of the disease matters. How easily does it spread? How quickly does it kill its suffers? Are there methods to treat, cure or vaccinate against the disease? It wouldn't be fair to compare leprosy or TB with the more virulent and deadlier smallpox for example. So we can hypothesize that healthcare workers are more likely to contract and die from diseases such as smallpox from their patients compared to TB or leprosy.

Leprosy:
Father Damien worked with lepers in the leper colony in the Kingdom of Hawaii for 16 years before he died from the disease himself at the age of 49. So he didn't gain immunity to it. We still do not know the mode of transmission and upto 95% of the population is immune to it.

Tuberculosis:
Lets take René Laennec (amazing clinician if you are interested) who invented the stethoscope and detailed the value of auscultation in diagnosing TB. He died of TB in 1826 at the age of 45 while studying contagious patients and dissecting infected bodies. However, his colleague Pierre Charles Alexandre Louis who used statistical methods to evaluate the progression of the various stages of the disease collected thousands of TB patient histories and autopsied hundreds of bodies (mind you he may not have cut the bodies himself) practiced for another 30 years until 1854 when he retired and outlived Laennec by almost half a century - he died in 1872 at the age of 85. However, we do not know if died as a latent carrier of TB. I'm going to go off on a tangent here.

Lets look at the efficacy of the TB vaccine - the BCG vaccine varies considerably. It's somewhere between 0-60% depending upon where and what population the study is from. With efficacy dropping off the closer you get to the equator. Infact in nations with endemic TB upto 70% of the population is thought to have latent TB (habor the bacteria but aren't contagious or symptomatic). So even though such a high percentage of the population acquires the pathogen they happily go about their lives without ever developing the disease.

It would be good to look at people who worked in sanatorias to see if there is any further. Like father Damien some carers (doctors, nurses, aides etc) may have died due to contracting the disease but these facilities were usually built to be open and preferably in drier regions or cool mountainous regions to reduce transmission via droplets.

I believe that even though TB and leprosy killed millions throughout history, healthcare workers did not have a significantly higher risk of death due to such diseases compared to the rest of the population.

Check out the history of [Puerperal fever] (http://en.wikipedia.org/wiki/Puerperal_fever), also known as childbirth fever. It took a while for doctors to realize that they were transferring the infection from cadavers and sick patients directly to women in labor. This man, [Jakob Kolletschka] (http://en.wikipedia.org/wiki/Jakob_Kolletschka) was a noted physician who died from the disease (despite being a man). He was performing an autopsy on a deceased woman and contracted the infection via a cut finger, resulting in a painful death shortly thereafter. His partner/coworker [Ignaz Semmelweis] (http://en.wikipedia.org/wiki/Ignaz_Semmelweis) was inspired by Kolletschka's symptoms to trace the etiology of Puerperal fever and pioneered antiseptic procedures to prevent transmission of diseases such as this.

I am certain that they had greater risk of getting infections but they knew some diseases could be spread from a person to another and took precautions.

Wikipedia on Plague doctor costume for more info on that. I think they looked quite awesome though maybe slightly scary/intimidating especially for children to be honest. I would of seen them more like reapers than doctors haha.

You should also know that very few small percentage of diseases are transmitted by air and that most are by touch. There are other stuff like disinfecting, gloves, washing hands and hygiene etc etc which easily prevent infection by touch. If they were good doctors then they would live like everyone else but you will find careless doctors so you would expect them to have higher mortality.

It is really vaccines that protect medical personnel from infection (Prevention is always better of course)