You'll have to sell your current house first, in order to get access to the $600K. (Also, the seller assumes realtor fees of 6%, so don't forget to subtract that from your equity.)
You'll need cash on had for the down payment (20%), earnest deposit (can be high, depending on how competitive the market is), closing costs. Also, factor in moving costs, rental fees (if you need to live somewhere else for a couple of months before moving into the new house), and funds for minor repairs and renovations (assuming that the house is essentially move-in ready). You'll need to furnish the house, too, since I assume that the new house will be bigger.