So I don't think you need to buy anything.
Your D-Link device will absolutely act as a regular access point and you can give it a different SSID in the cottage to the SSID of the router in the main house. See page 23 of the manual:
http://files.dlink.com.au/Products/DAP-1360/Manuals/DAP-1360_F1_Manual_v6.00(DI).pdf
Thank you for looking into this. I have not looked at the manual yet, but it sounds really promising. It would be great if I don't have to buy anything.
You've done the hard bit of having an ethernet cable run between the house and the cottage. If you need wired clients as well you put a cheap switch on the end of the ethernet cable in the cottage and plug the D-Link into the switch. If just wifi then plug the D-Link onto the end of the ethernet cable as it emerges in the cottage.
I think I am following what you are saying here. If I am not mistaken, I have this already, but I'm not sure. I have a D-Link DES 1005A Desktop Switch plugged into the the D-Link Network Adaptor. It looks like this:
Front - https://qwertypoint.imgur.com/all/
Back - https://i.imgur.com/f2mYhZb.jpg