I was in a similar situation, as my DD had a severe allergic attack at 6 months and I didn't know what I could give her...not great, I know.
Have seen various allergy consultants over time and the consensus seems to be that children can inherit a likelyhood of developing allergies but not normally the actual allergy of their parents. So if you have a problem with dairy/wheat in the family, it may well be that your child has an allergy, but it may not be to dairy/wheat, but could be pollen, nuts, latex, bee stings, you name it. For example, my DH has severe allergy to Walnuts, I have mild allergy to Penecillin - DD has severe allergy to Egg & Hazelnuts. This seems to be the common scenario.
Therefore the best thing seems to not specificly exclude wheat & dairy, but as tatt suggested, to introduce them one at a time.
If you're nervous, for extra comfort, try rubbing a bit of the food on the skin first, wait a bit (about 15mins) to see if anyting happens. Then start with a very small amount (pea size) to eat, wait a bit again, then a spoon full, etc. - this is what they do at the hospital when they test if a food can be tolerated.
Good luck!