Hmmmm... my understanding was that coconut allergies (eaten, not topical) are fairly rare? Coconut was suggested to us several times as a "safe" food/fat while we worked out dd1's allergies... and nearly everyone suggested it for dd2 when her weight dropped. We add coconut to a lot of meals because of this...coconut "cream" on oatmeal is a favorite with dd2.
But allergies are a good thing to think about when introducing foods to a young babe. Even without a family history you just never know, especially these days! For reference, the top allergens are:
Milk
Eggs
Peanuts
Tree nuts (such as almonds, cashews, walnuts)
Fish
Shellfish
Soy
Wheat
And the reaction may be subtle... a rash, eczema, red bum, under eye circles, cough, difficulty swallowing, etc. So while we're very gung-ho with self feeding I do keep a close eye on what the girls get and rotate items on a 3 day schedule due to dd1's dietary restrictions.