User blog comment:H-Man Havoc/Who is older, Jon or Dany?/@comment-5014364-20160630030204

Ned arrived at the Tower of Joy some time after Willem Darry fled Dragonstone to the Free Cities with Viserys and Daenerys. However, what point Jon was born relative to this is unknown - if Lyanna was dying from childbirth in the tower, Jon is probably younger than Daenerys by weeks or days.

However, his age is irrelevant to succession; he's the son of her older brother, no matter how old he is relative to her.