Sadly, there is no requirement at all for any child to be in a safety seat on a plane. However, if you have purchased tickets for both children, you are entitled to bring your seat on board. I got hassled some times by flight attendants who were clueless, but it is your right. However, booster seats are not allowed (although I have seen them on board) because for a booster to work properly, it is supposed to be attached with a lap/shoulder belt, and of course, there are no shoulder belts on the plane.
For thos of you reading this thread who have not purchased a seat for your infant or toddler, please know that most airlines will let you take the seat on board. DO NOT BE INTIMIDATED BY THE CHECK-IN AGENTS. Tell them that if there is no room for it, that you'll "gate check" it. (Same with your stroller....don't check it unless you want to.) Ask them if they can "soft hold" a seat in your row; this means that they will not fill that seat until the last moment. Some will be nice & cooperate; others will look at you like you are nuts. When you get to the gate, check at the last minute if there is an empty seat in your row. If not, ask for a gate check and then you will be allowed to carry the seat (or stroller) all the way to the end of the jetway & leave it there. It will be taken off the plane at your destination and left on the jetway for you to pick up. It is soooo convenient!
FYI -- these tips were given to me by a kind & wonderful agent at British Airways 8 years ago when we traveled to London with DD who was then 10 mos. old. I used these tips for at least 20 trips when she was a toddler and only once did I have to hold her on my lap. That trip terrified me so much that from that moment on, even though technically I did not have to until she was 2, I bought her a seat. DD rode in her car seat on airplanes until she was about 4 when she went into a booster.
Good luck!