Is it a virgin barrel? If not, you may not want to have something in it for 2 months. Remember that the surface area on a small barrel is larger in contact with a smaller amount of beer.
I am planning on getting a virgin barrel in the next month or so and was only planning on the first beer being in it for 2 weeks. I will follow that immediately with a repeat of the beer for 4 weeks and repeat it again for 3 months. The more you use it, the less of the wood flavors are going to come out of it, but early on it may over-power your beer.