Wouldn't the halving of the money supply cause doubling of value of each coin though?
Yes. If the total supply of all available bitcoins were to be cut in half (and the demand were to stay the same as it is right now), then you could expect the value to increase. Fortunately, the supply of available bitcoins is not being cut in half, only the rate at which new coins are minted.
Right now there are a total of 10,505,425 BTC in existence. Prior to yesterday, approximately 7,200 new coins were added to the supply each day. That is an increase in supply of 0.068536% per day. Now there are 3,600 new coins added to the supply each day. The supply is still growing only now it is growing by 0.034268% per day.
I think if I am understanding correctly that it would not halve the supply only halve the pace of generation and if more and more people are mining that may not even happen either. . .
No. The protocol is designed to ensure that a new block is created approximately every 10 minutes. If more and more people are mining, then the difficulty of the block is increased so that we still only get one approximately every 10 minutes. If people stop mining, then the difficulty is decreased. The pace of generation is half of what is was 2 days ago. It will remain at this rate for 210000 blocks (which works out to be a bit less than 4 years) at which time the pace of generation will be cut in half again. (and so on and so on until the block reward reaches 0.00000001 BTC).