Mostly safe to give. Years ago it was thought that delaying the introduction of certain foods would decrease the possibility of a child developing allergies. That is no longer the case. If there is no compelling family history of food allergies it is common practice to start diverse solids, including strawberries at about six months of age. As with any new food, if you see any reaction, discontinue it.
They can have them. There is no evidence that suggests that babies must wait until a certain age before receiving certain foods. If there is a strong family history in a first degree relative (parent, sibling) of a serious food allergy, then waiting until the child is older to introduce certain foods is an option, but not one based upon any data.
No reported allergie. There is no research to suggest that most foods- strawberries included- should be avoided in early childhood. The only exception might be in a family full of people allergic to many foods.