Nifty-Chicken, I happen to know the answer to many of your questions, since I was thiiiiis close to buying an existing goat brush clearance business right here in Malibu.
To answer your questions:
1) It costs us about $400 each year to do this. Would rent-a-goat be cheaper?
Depends on what you have growing and how much rain you get. Here in So. Cal, most people only need to have the goats in once every year to two years, and the woman I was going to buy the business from charges $125 a day (which is way too little I think for all the work involved, but much more than that and people just start hiring illegal workers instead because they are SO cheap. I know. Its awful.)
2) How long does it take a goat to clear 1.5 acres? Would it be safe to assume 2 goats would be half as long?
for 1.5 acres, the woman here will bring her whole herd of 12 goats, because the hard part is just putting up the fencing. Once that's up, its no harder to bring 12 goats than to bring 2 goats. Depending on how much vegetation you have, it takes the 12 goats about 2 -3 days to clear a lot that size. Whatever the goats don't eat is cleared out by hand.
3) The area is mostly fenced in, but there are some areas I'd need to close up. What kind of fence is required to keep goats secure?
She uses these large metal fences from Home Depot. They are secured with long landscape stakes that are pile-drived into the ground. They do have to be pretty tough fences because the goats will stand on them or try to go under them if they see something tasty (like your nice landscaping!) on the other side. Some of her customers have her come back every year, and so they will invest in good quality fencing that looks nicer than the temporary fencing. Then she can charge them less because all she has to do is let the goats in and check on them once a day.
4) Are goats noisy? We've got neighbors on all sides of the yard.
The goats were remarkably quiet while they were browsing, and would settle down and sleep at night. She has customers all over Malibu and Brentwood in densely populated areas and never had a complaint about noise. People love them in fact, and the kids really go nuts.
5) Where do I even go to get goats for this purpose.
I'd start with your city fire department. They usually have a preferred vendor list for goat clearance business.
Good luck and do it! I had so much fun in my few weeks of working with the goats. It kills me I couldn't buy the business, but it just wasn't profitable enough to make it worth quitting my job.