I'd bring the Radian on board with you, and buy another ticket so you can use it. Or leave babe home. It's not safe to have a lap baby for your baby's sake (they're either your airbag or a projectile), or for those around you (weight times speed equals force, and a 20 pound baby at 150 mph is 3,000 pounds of force heading to the back of someone else's head).
What would you have done if your baby was two? Whatever answer that is, apply it now, since the AAP, FAA, NTSB, and technicians don't recommend lap babies.
Then you also don't need to worry about your Radian.
The Radian does fit in the overhead. Checking it means it's crashed. Or it can be lost.
It'll also be easier for you to not have to share your three cubic inches with a child who doesn't understand, "The seatbelt light is on, everything has to be restrained now so we can take off/land, please don't get up, stand up, wiggle, play with your sibling, or anything else." Eating can be a challenge as well. Definitely bring a sippy cup for both kids and a water bottle for you, that way you won't get drink spilled on you since they only give either cans or big open cups that seem to want to tip over anyway. I do that, even without Laine in my lap. I just hand them her cup for juice/milk, and my bottle for as much water as they can give me.
Did you know the safest place for your little one during turbulence or an emergency is in a government-approved child restraint system (CRS) or device, not on your lap?
That's directly from the FAA.
http://www.faa.gov/passengers/fly_children/crs/
What would you have done if your child was two when you made this trip? Either not go, fly different times, or buy a ticket? Flying at different times is probably not an option right now, since you've already booked the tickets. So either do you cancel or buy another ticket? Call the airline and tell them you would like an infant in seat, and can they offer you any discounts? Maybe you won't have to pay 100%. It's worth a phone call.
Or I'd bring the Radian on board and hope for an empty seat in which to use it. And if not, stow it overhead.
Please buy a ticket next time. Protect the others on board.
Wendy