IMHO, I wouldn't replace the tires until you start having problems with them.
I've got >10k kms on mine with no major problems (knock on wood). I've had to get a couple patched though, I live in a new area with a ton of construction.
First thing I would check is the date on the tires (including the spare). Tires are only good for 5 years, according to the manufacturers. Then I would just make sure you inspect them as part of your pre-trip inspection everytime you travel. Check for nails
, then anything that doesn't look right.
I know that everyone wants to do the preventative measures, but I've read about the same amount of blowout/failure rates with other tires. So choose your poison.
With Trailer tires the issue is that they sit for soo long, then are typically scrubbed (slide sideways) to get into a spot. Neither of those are good for a tire. Problem I have, is that you have to take everyone's experience as a grain of salt, and the internet being the way it is, you are going to read about more bad experiences than good.
At any rate, I wouldn't worry too much about it.