That's the Traveling Toddler you're talking about. I have a friend who swears by it, and many people here have used them. I'll be getting one for our new babe. Very awesome.
At 18 months she can ride rear facing on the plane, unless she's over 35 pounds, and that will make it MUCH easier to install the seat. You don't need the belt extender rear facing. A big Britax is a hassle and a half forward facing, so as long as you can put her rear facing do it. Just that much easier.
I've flown solo with my daughter and her Britax quite a lot. It's not as bad as you think it'll be.
She can ride in the seat in the airport, then you just take it off to get on board. Let her on the plane in front of you. She can't get off the plane, so if she wanders that's fine. She can't go anywhere. Or, she can do what my daughter does and curl up under the seat in front of her spot so that way she's out of the way but right near me. Rear facing just put the armrest up, then thread the seatbelt through the beltpath, right on top of the cover. It'll take two seconds, unless you have trouble getting the buckle through the cover (it'll stretch over time).
Current regulations have changed that carseats do not have to be near the window, but personally I'd feel better with a rear facing one there so I don't block anyone. Forward facing, depending on the seat I wouldn't be as bothered. Most flight attendants don't know about the regs change, though, and will simply reseat anyone at the window for you. It's not a big deal. Though see if you can get a window and aisle seat assigned to you, since the middle is the last to fill up. You may get three seats for the two of you.
Safe travels!
Wendy