Isla:
Home schooling offers many advantages and disadvantages. Here are my views from our experience:
Advantages:
1. Kids get more sleep if home schooled.
2. They spend less time on the highways and in school buses.
3. They learn at their pace. No need to wait for the slowest kid in the class to "get it".
4. They bond strongly with the dominant home schooling parent. (see Disadvantages!)
5. They can learn almost anything-they aren't hamstrung by a "canned" curriculum. If you want to teach them French Existential Philosophy, or the poetry of Pablo Neruda, and they want to learn it, you can. Public education fails miserably in this regard. Everyone's crammed into three or four "molds". The truth is a kid who loves to fix computers might also like to learn Russian. A math whiz might like to learn to type, or cook. This is the single greatest strength of home schooling in my view-its flexibility. It really teaches kids that they can learn anything they want to learn. The benefits for the rest of their lives are obvious and enormous.
6. As a consequence, most home schooled kids receive a much better education than the average kid. Certainly, they generally do better academically than their public school peers.
7. Your daughter won't come home and call you a dumb motherf*cker. She probably won't get stabbed, unless you lose your patience.

She won't be pressured to have sex every 40 minutes. She won't have to put up with the snotty teenage girls, many of whom could be strangled on the spot without further ado. She won't have to put up with the daily rejection by immature teenage boys who think she is flat-chested, big-butted, freaky, too shy, too loud, too tall, too short, too ethnic, etc.
Disadvantages:
1. Home schooling requires a smart, well-organized, and dedicated set of parents. Inventory the skills you and your husband have available. You must feel confident, and reasonably so, that you have the ability to educate a high schooler. Home schooling at the elementary and middle school levels is an order of magnitude easier than high school. In short, the level of committment is enormous. Most parents don't measure up. By way of example, my daughter has been homeschooled for two years. She will be skipping the 8th grade and going into the 9th grade at a local math and science oriented high school. Although I feel competent to teach her math through trig, and high school biology, I would fail miserably at AP chemistry, French (even though I've had about 5 years of it), AP calculus, and AP English. We've decided we don't have the skill sets necessary to do the job. Your daughter's needs will certainly be different, as will your abilities.
2. Girls, in particular, miss their school friends. They tend to be much more interested in friendships, in my view. My daughter has complained about this problem. She is looking forward to getting out of the house and spending time with her peers. (See Advantages, above.)
3. Home schooling parents tend to be right wing Christians, a group I consider pathological. They can be cloying, annoying, and single-minded. I know only a couple of Catholic families that are home schooling, but even in that segment growth is occuring. You will probably want to join a local home schooling group, most likely made up of shibboleth ridden right wing Christians. They WILL help you do the right thing for your child. You will have to listen to the joys of creation science, and the never-ending verities of the Bible. We have had to keep our mouths shut most of the time when at meetings with them.
4. A teenager WILL drive you crazy at least half the time. The hormone thing has just started here-my kids were all late bloomers-and I'm absolutely certain three or four times per week that I could kill my own child. You have much more patience than me, and are much, much, kinder. Success is possible, relationship-wise.
5. The cost of home schooling will come as a bit of a shock. Books, software, trips to the Dali Museum (lucky you), etc. We typically spend about $2,000 per year. Cheaper than a private school, but not inexpensive.
6. Home schooling can put a strain on your relationship with Mr. Isla. Is he ready to teach math, science, English, history, etc.? He will have to share a good part of the load. You can't do it all. Don't even think you can. He MUST be 100% supportive and READY to jump in and help. In my family, my wife handles Violin, English, History, Bible (yes, we do that), and French. I handle math, science, French and writing. Math consumes the most time, so I have my hands full. Both parents must give up quite a bit to meet the challenge. Is he ready, willing and able?
Only you know whether your daughter's decision is well-reasoned or the product of emotional lability.
Good luck.
Dominus vobiscum.