I'll answer the questions in the OP's post one at a time.
Is it a good idea to bring a keg of beer to an 18 year old's birthday party? No. Even if it's legal in the jurisdiction in question, the person most likely has a very poor ability to regulate their alcohol intake and will in all likelihood end up embarrassing (or even injuring) themselves. And how much do 18 year old girls like beer anyway? Not very much. This is nothing more than a vanity play on the OP's part, an excuse for him to point to the keg and say, "Look what I made!" This day is not about you. It's about your sister.
Is it a good idea to transport alcohol across state/provincial/international borders? No. It's actually illegal.
Is it a good idea to bring a keg with me on a plane? No, for many reasons. You obviously cannot bring it on the plane with you as a carry-on (Liquids of more than 4 oz are prohibited, and it's both too big and too heavy to fit in the overhead bin). So you'd have to check it. That means a $25 checked-bag fee. Also the TSA forbids many different types of cargo, including pressurized liquids, so this is probably a moot point. But even if they took it, you risk someone losing or damaging your keg. What if someone bumps a poppett and sprays beer in the baggage handling area? What if it shifts during turbulence and gets punctured, spraying beer all over the inside of the baggage compartment of the plane, damaging (at best) other baggage, or (at worst) sensitive avionics? If your keg bursts in the cargo hold, do they tase you immediately, or wait until they make the emergency landing and arrest you?
How would you serve the beer once you got it there? You'd have to bring a CO2 tank, and good luck getting THAT on a plane. How will you get the keg back home? Pay another $25 checked-bag fee? Now you're in for $50 just in baggage fees, assuming everything else goes smoothly. It's not cost-effective.
What if the beer is bad? You could be turning a bunch of new drinkers off of craft/homebrewed beer, doing damage it will take years to undo.
Is it a good idea to try my hand at kegging for the first time, for a teenager who probably won't even drink it? No. You've never kegged before, and want to start with a rushed batch and myriad unknown legal complications?
Is it possible to produce a decent batch of beer in 5 weeks? Yes. That's more than enough time to brew a nice, moderate-gravity pale ale.
- Days 1 - 14: Primary ferment
- Day 15: Rack to keg, cold crash under 10 psi CO2 pressure
- Days 16 - 20: Fine with gelatin under 10 psi CO2 pressure
- Days 21: Draw off first pint or two of cloudy beer. Then rack to a fresh keg, pushing it with CO2 and using a beverage-to-beverage keg "jumper," optionally through a 1-micron filter.
- Days 22 - 35: Keep keg in fridge under 12 psi CO2 pressure to finish carbonating
And that's without cutting any corners. Heck, I bet I could turn around a fully-carbonated, clear keg of beer in 2 weeks if I really had to. Hmm... that sounds like an interesting experiment/challenge.
- Days 1 - 7: Primary ferment at 65° F
- Days 8 - 12: Bump temperature up to 70° F to finish
- Day 13: Rack beer to keg, then push through 1-micron filter into a second keg. Put keg in fridge on 12 psi CO2.
- Day 14: Shake cold keg at 12 psi until desired carbonation level is reached.
Voila! Cold, crystal-clear, fully-carbonated beer.
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