first you need to see, agree to and sign a rental agreement. Get the owner's phone number and talk to him/her. Then (if you still want to go through with it) go to your bank and get a US cashier's check which you tell the owner is the US equivalent of a money order. He/she will take it to their bank and cash it. Now for getting it there.... cashiers checks are not well traceable, so you want to send it by some method where the recipient has to sign for it so you have proof of delivery at the other end. You also are just one month away.... sending it US registered mail will take too long. Sending it Fedex or UPS will be pricey. I guess you could do a wire transfer, but those have gotten a bad rap lately with scams. Or if they live locally you could pay cash on arrival (but they may not want to hold the dates without money for that long). Also for the record, credit cards or PayPal will charge the owner a fee (being international, probably about 4% depending on their merchant agreement).

Are there any other places in the vicinity that look decent, have availability, the price is right AND they take credit card or PayPal?

As an owner I wouldn't want to hold dates a month out, waiting for a cashier's check to arrive, what if it ends up being forged or never arrives? Ask for a phone number and call them for clarification. And GET A RENTAL AGREEMENT. And have a great holiday!

This owner has very likely been renting their property successfully without a written agreement.  There are some owners, and renters, that are comfortable with what I would term a "casual" agreement.   If both parties are satisfied, I suppose it works.

But it's not clear to me how a rental works without written terms when anything out of the ordinary arises.  And reading through this forum will provide many instances of unexpected issues for owner and renter.

As an owner, I want my guests to be fully informed about all aspects of renting my property.  As a traveler, I want to know the provisions/amenities of the the property and the expectations the owner has of their guests.  How does this owner convey this information? 

Is there a cancellation policy?  Is a security deposit required?  How is it returned?  Under what condition is it charge?  Is there a local contact in case of a question about or problem with the property on arrival? 

What is included in the rental?  Linens?  Parking pass?  Pool privileges?  How is all of the day-to-day information conveyed?

There may be an on site management company handling the day-to-day responsiblities of the property and that may be why the owner does not feel a written agreement is necessary.

If you can find another property that suits your needs AND provides a more structured transaction, I think it wll offer you more protection.  But, if you are set on this property, ,it is likely to be fine, until it isn't . . . .    Consider purchases made on cordial, perhaps friendly terms with the seller, which become adversarial when the product is damaged or fails (I just had a long and painful negotation over a washing machine.  Very painful.)  Without a written agreement there isn't any recourse (it's challenging with a written agreement . . . ).

In all my traveling, throughout the US and Europe, I have never come across an owner that does not offer a rental agreement.    In every instance the owner sent me a copy of the agreement so I could consider the terms before making a decision about renting.   In my opinon, as with any other purchase, the buyer should be fully informed of the terms. 

All the best working this out.