Your wife's concern about any possible transmitable disease to your child shows her concern and care. Here are some thoughts for you:
1. Research the 'number of cases' of those diseases on the internet and possibly the percentage of the population that is infected
http://cid.oxfordjournals.org/content/24/6/1195.full.pdf
http://www.rightdiagnosis.com/t/toxoplasmosis/prevalence.htm
2. Look up the 'boy in the bubble' -- the child had no immune system and couldn't be exposed to normal environments
http://en.wikipedia.org/wiki/Boy_in_the_bubble
3. Remind her that children have and develop a strong imune system from what they encounter in their environment. For example when Small Pox was deadly, people who lived on farms and had encountered a milder form of pox called 'cow pox' had immunity to small pox
http://en.wikipedia.org/wiki/Cowpox
Last and not least hygine, and developing the hand washing habit after touching animals may provide a really good life lesson for your child/children and establish valuable habits that would help them be disease free.
Not to burden you with links. The points I am aiming at are that the diseases are considered rare, isolation is not a good way to develop an imnune system, and lastly, some contact with animals can be beneficial to humans to actually prevent diseases.
In the end if she doesn't come on board, (and I don't know the ages and general health of you kids) you probably have to delay having chckens.....but hopefully it will become a fun activity for your whole family.