The Toyota Extra Care Platinum Plan is an extended warranty, that covers unexpected breakdowns (an extension of the basic new vehicle warranty). Some responders are confusing it with a pre-paid maintenance plan (where you pre-pay for regular services, such as oil changes/tire rotations).
You can purchase the Toyota Extra Care Platinum Plan anytime up to the end of basic 3-year/36,000 mile basic warranty. You can buy it from any Toyota dealer, not just where you purchased your car, nor where you have it serviced. You can (and should) negotiate the price.
Even at $1500, I wouldn't buy the plan from your dealer. Toyota's MSRP for the 6 year/100,000 mile/$0 deductible Platinum Plan for the Corolla is $1200. There are plenty of dealers that'll sell you the same plan for MSRP, and if you shop around you'll find others that'll sell it to you for LESS than MSRP.
http://www.toyotafinancial.com/consumer/tfs.portal?_nfpb=true&_pageLabel=pg_VSAPricing&carSelected=Corolla
For an example of how shopping around can help you out, I'll use the Toyota Prius. The MSRP for the longest-term (most expensive) 7 year/100,000 mile/$0 deductible plan is $1850 on the Prius, yet there are several dealers that will sell this same plan for <$1000. Shorter term plans (such as your 6 year one) are even less expensive (<$800).
More info (a little dated, but...): http://vfaq.net/docs/ExtendedWarranty.html
So no, I would not get the warranty from your dealer, unless they offer it to you for a MUCH lower price.
Is the relocation assistance and towing worth it to you to get the warranty plan now, as opposed to waiting to closer to the 3 year/36,000 miles from the vehicle's in-service date/mileage to see how your car's reliability has been (or other Corollas of the same vintage)? If you can hold off, I'd suggest putting that $1500 in a high interest-bearing money-market or CD account so that you can purchase the same plan later.
Or do you really need to roll this warranty into your bank financing?
If you need the peace of mind, or would have trouble paying for an unexpected breakdown should one occur during that 6 years/100,000 miles, then I say go for the extended warranty. Just get it at a better price.
(However, if you were asking about a 3rd party warranty from someone other than Toyota, I would say to completely avoid it as a waste of money. Same goes if your dealer says that you can get all your money back if you don't use your plan by the end of the term, as that's an additional insurance not from Toyota... At least the Toyota dealers are used to the Toyota Extra Care plans, all dealers will work with them and get all the preapproval and paperwork done for you and will get directly paid by them (so you don't have to apply for a reimbursement from the warranty company). And you know that the Toyota warranty company will still be around later should you need it... I have never heard of them not approving work, unless you have done some non-factory mods to your car's system that is having problems...)