I personally would not, the stress from travelling and showing may cause an early birth. Shes working hard enough to make you babies, Iwouldnt ask her to show too. One of my friends had a very seasoned show doe they took to a local show for a day and she went into preterm labor from the stress and lost a baby. The other baby lived but never did well.
However, if your doe is used to going for rides alot, like mine goes with me at least 2 or 3 times a month, then maybe she'll be ok.