I had my cats chipped with the Home Again chip. I ended up not bringing them with me for other reasons, but it should have worked fine.
You do have to have the rabies verification, though. I had to get the vaccination, then have blood sent to an approved lab for testing. There are only 3 or 4 approved labs. Be sure to read the DEFRA information carefully in that regard.
Fortunately, I lived near one (University of Kansas, I think). There's also one in Texas. Can't remember the others.
Just be sure your vet understands that process.