Medium range RFID module suggestions

I'm helping a friend build an automatic dog door. He would like it to open when his dog stands nearby and he thought RFID might be a good option. Researching, I see plenty of suggestions that high frequency (13.56 MHz) readers and passive tags can have a range up to a meter, so I think this is feasible, but nearly all the modules I find have built-in antennae and are limited to 10 cm range.

I understand that I may have to build and tune my own antenna (which I think I can do if necessary). Are there any suggestions for inexpensive RFID modules that I can attach an external antenna to?

Thanks!