Well, as someone who had travelled successfully with a dozen birds of various ages in the bed of a pickup in the rain for fourteen hours, I can assure you that 90 minutes is nothing, and I can tell you various ways to do it that will make you feel better about their safety. Chickens travel extremely well, you just have to make sure whatever they are being carried in is secure somehow from tipping over, etc.
Please don't think I'm making light of your concern, but I think that you might be worrying about the wrong things. The best thing you can do is what you are doing right now - building to coop before the birds arrive. Too many people don't. Also, be careful about being so eager to get birds that you buy the first ones you find just to have SOMETHING. All the rest of us have done this at one time or another, but it can backfire badly if you're not careful. Believe me that I am not trying to plug our show when I say this, but it's true: you will not find a better selection of good quality, healthy birds than at a sanctioned poultry show like we have. (I say this to differentiate from the county fairs and others not associated with the APA or the ABA, or swap meets, etc.) Only at poultry shows will you find breeders committed to the betterment of their breed. That includes keeping healthy birds that best represent the standard for their chosen breed.
If you don't want to wait until our show, there are several others near enough to you that you can attend. I am meeting several friends at the Delmarva Poultry Show on March 31, in Harrington, DE. That's a wonderful show. There's also the Susquehanna Show, and a couple of others in the next few months. Your best bet for getting the started birds that you want is to post on the threads of the breeds you like and ask the folks there if they are attending any of these shows. That's a great way to get birds that are otherwise too far away for driving, and to meet some great breeders. The best advice I can give you if you have a breed you desperately need is to WAIT until you find the right breeder - that was one of the hardest lessons for me to learn, and one of the best. It's SO hard to wait, and SO worth it.
I'm not at my own computer right now, but if you like, I can post a couple of links that list the poultry shows so you can see how close they are. And don't let the distance worry you - the birds can handle it, especially the ages you are looking for. If day-old chicks can travel across the country, started birds can spend a few hours in a carrier with no problem. We had a little cochin bantam hen in a cardboard box a little bigger than a six pack for about fourteen hours on the way back from Indianapolis. We cut out a couple of windows, and put a little dish of food in there, and she was totally fine. Probably better, in fact, than the big orpingtons who had plenty of room to tip over when we turned a corner.