I would transport him in a padded box, either a pet carrier with small holes or a shoebox with holes. You might want to let him spend some time in the box prior to moving, so he gets used to it. Try to keep temperatures moderate at all times. Make sure you have a set-up ready for him when you get to your new home.
Yes, he should be fine for 45 min., but try and keep him out of direct light or in the path of air conditioning. Yes, those things should be common sense, but maybe they aren't. Thanks for asking. I hope your move goes smoothly.
i moved all mine 1 hour drive to where i am now .this is what i did i used a old shoe box poked small pen holes in it , rubber banded the top of it to the bottom and made sure they were on a pillow so the bumps and things would be easier , i also made sure they has a few crickets and a soft padding like paper towels and a toilet paer romm cut in half for them to hide they will be fine but as soon as you can get the tanks set up and have them back in thier home they will be fine trust me all 9 survived