Is it okay to have a torah aliyah during the 11 month mourning period, or should one wait?
I think you will find that there are various customs. Some communities give last aliyah (acharon) to a mourner who then says half Kaddish.
Rivivos Efraim 5:556 concludes that although there is no Chiyuv for an Avel during the 12 months to get an Aliya every Shabbos, it is a good idea if possible. Thus it seems clear that an Avel should get an Aliya if possible during the 12 months.