Ditto to all that kmsgameboy said
I'm also new to this but (from what I've experienced so far, at least) there are a few other things I personally keep in mind when bringing mantids out of the house for long periods.
Firstly it's best to keep a regular lighting cycle (for nymphs especially). One reason is that they generally time their moults to occur at night and unnatural deviations from the day/night cycle throughout their instar could confuse their internal clocks. Plus, one of the worst things that could happen is if a bright light suddenly comes on (and the car starts up and ppl are moving about etc) while a mantid is moulting, and the chap freaks out and leaves part of a limb behind in its hurry to extricate itself. Like what kmsgameboy said, it would be better to leave it at home if it's due to moult soon but sometimes that isn't possible.
Also, mantids are highly visual insects and it'd be a good idea not to to expose them to loads of movement or external stimulus (like at the car window or beside you while you're driving). They'd tend to get stressed.
Another thing is how you're going to be able to feed them. Unless you bring feeder insects along with you, you're probably going to have to stop at a bush / field once in awhile to see if you can catch any (if you're desperate enough you may find yourself raiding the fruit/vegetable section of any grocery store for flies...)
All in all, if you have someone to feed/clean up after/water your mantis at home while you're gone, it'd probably be a better idea than bringing it with you. But if you don't, leaving it alone for a week without food or water is really very risky.
