Encrypt your private key with a long password and decrypt it on the target computer. Here's how:
First, export the public key:
gpg --output public-key.gpg --export {KEYID}
Then export the secret key and encrypt the result before it's written to disk:
gpg --output - --export-secret-key {KEYID} |\ gpg --armor --output secret-key.asc --symmetric --cipher-algo AES256
Use either a very long or just entirely random password for the encryption.
Then transfer the keys.asc on a FAT-formatted flash and shred them afterwards, or if you know how to destroy CDs (ENTIRELY), use a CD and then destroy it.
To import the key on the other machine, run:
gpg --no-use-agent --output - keys.asc | gpg --import
This will prompt for your password, then decrypt and import the key.
Make sure you destroy the encrypted file after running this! On a small file like a private key bruteforcing the password is fairly trivial and can be done in a matter of weeks to months depending on the hardware available to the attacker. The attacker's job is further simplified by the fact that the structure of a PGP private key is publicly known, so known-cleartext attacks can be attempted. If the encrypted version of your private key is leaked, revoke the key and generate a new one IMMEDIATELY.
Source for the commands: http://montemazuma.wordpress.com/2010/03/01/moving-a-gpg-key-privately/