Chosen Solution

Can I transfer data directly from the old hard drive to the new one ?

Yes! You should be able to us an external hard drive enclosure and a free downloadable program called SuperDuper to clone the old hard drive to the new hard drive. You will need a different hard drive enclosure than the one I linked you to because the MacBook Air HDs have Zif connectors instead of a SATA connector. You can find the enclosure you need through a quick Google search.