I've traveled some with my daughter without my husband and it's definitely more challenging. You don't realize how much there is to juggle and thinking about.
You can take more baby liquids (milk, formula, juice, etc.) than they allow passengers without babies. So you're not limited to 3.5 oz in a zip lock, etc.
Strollers are a must. I made the mistake of not taking it one time and I was surprised how tried my arms got holding her on one hip and pulling a bag.
Try to pack everything in one rolling back.
Personally, I don't think you'll need to buy an extra seat for your daughter. Most flights, unless they are booked, will seat you in an empty row. 3 hours isn't that long. I've been on worse (14 hour flights). And depending on your flight time, your daughter might sleep most of the time.
I recommend having your child suck during take off and landing to help take pressure off your daughter's ears. She can suck on a milk bottle or pacifier, etc.
Also, my daughter loves music, so I took my MP3 player with me and head phones that wrap around the ear (not plugs that go into the ear) and put them on her during the flight. She loved listening to the music. Of course, she also had fun taking them on and off, but it was just entertaining her and that is the key. It also helped smooth her to sleep and distract her from all the weird airplane sounds.
Don't stress. Kids feed off our anxiety. Get to the airport early enough so that your don't have to rush or feel stress but not so early that you're waiting for hours.
Good luck.