Back then was a 9 year old and 1 day boy allowed to do yebam to his dead brothers wife?
Yes. However, it's not considered "real" yibbum; any relations that they have until he reaches the age of majority (13 years old) don't change that status. (So if they don't have relations after he reaches that age, then dissolving this marriage requires both a get and chalitzah. On the other hand, if they are intimate after he reaches age 13, then the yibbum fully takes effect, and only a get is needed to end it.)
(Shulchan Aruch, Even HaEzer 167:2. Rambam, Laws of Yibbum and Chalitzah 1:16, seems to say that in the first case only chalitzah is needed.)
Thanks to @DoubleAA for pointing out my mistake in the previous version of this answer.
See Kiddushin 19a, where the Gemara derives from a pasuk that there is no death penalty for relations with a woman married to a nine-year old through yibum.
Also see Yevamos 96b, where the Mishna states that the Yibum of a nine year old is a weak marriage- if he dies she still needs chalitza from the other brothers, but she can't do yibum to any of them, as she had already "married" the child. (In a normal case, after yibum she would become the yavam's wife entirely, and would not need chalitza upon his death.)
There are three approaches to understanding this:
1) Rashi: Min HaTorah yibum works fully, but there is no chiyuv misah. MideRabanan it's reduced to a weak marriage, as per Yevamos 96b.
2) Tosafos: The yibum has no effect at all, mideRabanan it's upgraded to a weak marriage.
3) Ramban: The yibum is partially effective.
All agree that the relationship is permitted, as mentioned in a previous answer. See Yevamos 111b, Yevamos 96b Tos. sv nasah.