WFT's are very intense terriers and will instinctively chase small creatures and respond to high pitched noises like crying. However, generally speaking they are friendly, confident dogs who can live happily, under supervision, with children. Like most wire haired breeds, WFT do not moult (or moult very slowly) however that does not neccesarily mean that they are good for allergy sufferers. Most people with allergies are actually allergic to the dander (dead skin and coat debris), not the hair - all dogs have dander and therefore may affect a sufferer. Also many people are allergic to the dogs saliva - if the dog licks itself the saliva will transfer itself to the hand of the owner, who will suffer a reaction.
Like Lapsedrummer, I own an Irish Terrier. The Irish are alot bigger than the WFT and therefore more difficult to handle. Depending on their upbringing they can be very good with children (however, many are not good with other dogs and this may cause difficulties if you are trying to push a pram and walk the dog at the same time). Irish Terriers require early socialising with children and other dogs otherwise they can be real hotheads 
- that being said I wouldn't be without one.
WFT (and Irish Terriers) require handstripping to maintain a healthy coat and skin. Handstripping is very timeconsuming and you may find it difficult to find time when you also have children to look after. However, a handstripped coat will help alleviate some of your allergies, as handstripping removes much of the dander and dead hair from the coat.
Have you checked out Soft-coated Wheaten Terriers and Welsh Terriers, they are non-moulting so may also be suitable for you.