This is going to be difficult as you are kind of "out of season" at that time of year. Certainly October is usually warm enough to be tramping around outside, but it can be a bit chilly particularly as you get into late October.
Renting a car and driving is really your best option -- from Washington DC is't about 90 minutes. This has the added advantage of allowing you to really see the battlefield at your own pace as it's a rather large area spread out over the entire area. It's not something you "walk" around.
If you're set on trying to do this using only public transportation, then the best way might be to use Amtrak from Philadelphia. Weekdays there is a train which departs 30th Street at 5:25am and arrives in Harrisburg at 7:10am. You can then grab the weekday shuttle (no weekends) called the Rabbit Express outside the train station to Gettysburg which departs at 7:18am or 7:42am (there are only two shuttles in the morning and two in the afternoon as it's a commuter shuttle) and arrives in around 9:00am.
Return trips from Gettysburg in the afternoon leave at 2:05pm and 3:00pm which would allow you to connect to a returning Amtrak train in Harrisburg to Philadelphia at 4:30 or 5:35pm which gets you back to Philadelphia at either 6:25pm or 7:23pm.
Cost right now looks to be around $30 each way ($27 each way on Amtrak and $3.50 each way on Rabbit). Search for Rabbit Transit Harrisburg on the internet to get more information.
That would be a quite compressed day, so you might want to consider an overnight in Gettysburg and catch the morning commuter out of Gettysburg to Harrisburg to do your return.
There is a local trolley which will get you around Gettysburg town although I don't know the schedule, and the visitor center at the battlefield beside being an excellent museum has a battlefield tour bus -- but I don't know the hours and if it's seasonal or not.
Keep in mind that the distance to Gettysburg from Washington DC is about half the distance from Canberra to Sydney, and from Philadelphia to Harrisburg is about 2/3 that distance. Philadelphia to Gettysburg is about the same drive time as Canberra to Sydney.
Edited: 9:17 am, July 07, 2013