Goat's milk contains about the same amount of lactose as does cow's milk, so it is not a good substitute for those with lactose intolerance. This remains true no matter how many times goat's milk advocates make the claim.
However, goat's milk does contain a somewhat different set of proteins than does cow's milk, so some people who can't drink cow's milk because they have allergies to casein proteins can drink goat's milk instead.
That doesn't mean that goat's milk is hypoallergenic. People can indeed be allergic to the proteins in goat's milk.
A study, Goat's milk allergy, by B. Tavares et al. (Allergol Immunopathol (Madr). 2007 May;35(3):113-116.) has the following abstract:
BACKGROUND: Goat's milk (GM) allergy not associated with allergy to cow's milk (CM) is a rare disorder. Caseins have been implicated as the major allergens eliciting symptoms.
METHODS: We report the case of a 27 years-old female patient that experienced two episodes of urticaria [hives] related to ingestion of goat's cheese (GC). She tolerated CM, dairy products and sheep cheese. Skin prick tests were performed with GM, CM, bovine casein and alpha-lactalbumin and fresh milk and GC. Serum specific IgE to GM, CM and its fractions, and GM and CM immunobloting assays with inhibition were also evaluated. RESULTS: Skin tests were positive to GM and GC and negative to CM. GM immunoblot showed an IgE-binding 14 kDa band that was totally inhibited after serum pre-incubation with GM.
CONCLUSIONS: Allergens other than casein can be involved in allergy to GM. Even small quantities of protein can elicit symptoms.
Rare, but possible. Goat's milk allergy is not a serious problem, but as the popularity of goat's milk grows in the U.S. it seems likely that the incidence of people finding themselves allergic to it will also grow.