First off, DON"T start solid foods at 2 months! Babies who start solids earlier than recommended are more likely to have food allergies and their digestive tract is not mature enough to handle them. Second, this is very common at this age. In fact, it is not normal for a 2 month old to sleep through the night and more likely the baby would die of SIDS. What ever you do, don't listen to anyone who tells you to put your baby on her tummy. Yes, they will sleep longer, but it increases the risk that they won't ever wake up (SIDS).
I would suggest sleeping with your baby (if you are a non-smoker and do not sleep on a waterbed), and breastfeeding through the night on your side. If you are not breastfeeding, it may be a little more difficult, but babies will often sleep more soundly if next to mom. Despite the current recommendations in the US not to sleep with your baby, it is still safer than sleeping in a crib. Check out research by Dr James Mckenna.
If you are not comfortable with co-sleeping, put your baby close by in a basinet and offer a pacifier. The pacifier will enable that suck swallow breathe pattern that the baby would have while breastfeeding, and the baby will sleep better. If you are worried about baby getting attached, you can always take it away within a couple months or only offer it while sleeping.