Hi Irfan,
I assume the relationship between Opportunity and Quote Product is as below. Please correct if my assumption is wrong.
Opportunity --(1:N)--> Quote --(1:N)--> Quote Product
Your requirement is to map Primary Solution Division and Opportunity Category from Opportunity to Product Division and Product - Category in Quote Product respectively.
To achieve this, you can use both option 1) & 2) or only option 2) below.
1) Client side, you need to create a javascript function onload of Quote Product form to fetch and update these two lookup fields from Opportunity via Quote.
2) Server side, you can create a plug-in on pre-create (preferred) of Quote Product to fetch and update the lookup fields from Opportunity via Quote.