I used an external hard drive for my backups via Time Capsule. I bought a new computer and I want to transfer all my old fonts over to the new one but when I go into the Font Library from the hard drive backup but my downloaded fonts aren't there?

The answer to that would probably be "Yes." If you don't remember where your fonts were stored, you may want to search your backups for any of the font files you know the names to. See where that takes you.

Ideally, Font Book and other font managers will temporarily store the fonts you "installed" into the System when you run the OS. When you shut down, etc. they are removed and reloaded on restart. The permanent place fonts reside is where you saved them when or after you downloaded them. I typically create a Resources folder on the root level of the computer and place a Fonts folder there. Then I install fonts from there, and they are available to all users on that iMac.

Perhaps if you did not have that kind of a strategy, perhaps many of them are still in your Downloads folder?

I am slowly transferring information fromt he backup to my new computer

Why are you doing it that way, as opposed to using Setup Assistant or Migration Assistant?

OS X: How to migrate data from another Mac using Mavericks