The push westward started in earnest after gold was found in California in the mid 1800s. By that time there were fabric mills on the east coast producing a lot of cotton fabric in a wide range of colors. Since the American Civil War was in the earlier part of this era, that would allow you to use any of the reproduction fabrics and patterns from that time, and they would be quite authentic. If we are to believe old movie westerns, a lot of saloons had sleeping rooms upstairs for all the cowboys and sheriff's posses passing through, so it wouldn't be out of the question for a quilt to find its way downstairs on a chilly morning.
You can read a bit about the history of the Turkey red dyes that were available by this time here:
http://hartcottagequilts.com/his3.htm , and that page also has pictures of period fabrics.
Here's a site that has pictures of quilts from the Shelbourne Museum, which might give some inspiration:
http://pioneervalleygirl.wordpress.c...a-more-quilts/ There is a picture of a quilt from the 1880's to 90's that has scrappy strings, which seems as if it would be more typical of the ones that travelled westward than the less sturdy and more precious decorative quilts from the East Coast, such as the Baltimore Album patterns, since the well-established folks were less likely to pack up a wagon and leave their homes. Still, probably the decision to bring something out west with them would have been an individual choice, and a pretty quilt inherited from Grandma would not have been left behind. So you'd have a very broad range of possibilities. The last of the lower 48 states were added to the union by 1912, so really anything before that period would be possible.