There are a lot of rental opportunities in Indianapolis, TH & SFH alike. My husband and I relocated here about 3 years ago from the Chicago area as well. You will find things in the MLS (we call in the BLC here), however there is an abundance of opportunities for rental that are not listed there as well. You can search on craigslist, forrent.com, rent.com, hotpads.com, or any of those sites. Depending on where you want to look in the city there are some specialized sites as well like rentbroadripple.com.
As Agents we can only show you houses on the BLC, but the first thing you really want to do is know where you are looking in the city, or if you are looking for areas outside the city. Being from Chicagoland I can give you a good idea of what will be comparable to Chicago areas. I would suggest getting a feel for where you want to be, and then really taking a deep look about 2 months out.
Keep in mind that most TH and SFH for rent do not sit on the market for long, Indy's rental market is hot and things move quick. If you look to early things will not still be there, but you want to make sure you give yourself time. When we relocated we found this out. We moved in 2 weeks after finding the place, landlords here want to get it filled quick and they won't hold the property.
Give me a call, or send me and email. I'll be happy to help.