Because of how the blogs are managed as their own forums due to the loss of a proper blog add-on, the most that I believe can be done is requesting some viewing permissions and restrictions on your own blog section. Unfortunately it would have to be all done manually, unless there is a way to have a hidden usergroup made that checks the age listed on your birthdate, and then only have that usergroup able to view the section.
Though that's all hypothetical about how implementation would work, though I'm not sure how necessary it is for an age restriction. The Mature Discussion board is viewable to all signed in members and if the topics are too heavy for someone, regardless of age, they can page off (or even request their access to be revoked).