It always depends on your domain registrar, that what options he has enabled for your with how many optimal features, you should send your NS area screenshot so anyone can guide you properly so you could get rid from that issue.
@fwh your point is also valid, but after moving to good registrar, because which registrar create hurdles, always annoying you until you leave him for the peace of heart
after moving, when all things in your hand, cloud-flare is master piece
@Dr. McKay no there is no risk, domains and site will remain active and available while transferring period.
i have also transferred few domains from internetbs.net to namecheap.com it was smooth shift in 4 days..
@portuguesedudeSir, add me on skype, i will try to resolve your issue, my skype id is imrelease.com_1
or if you wana do itself, ask your domain registrar to send you Auth Code, once you get it in email, go to name cheap, Click on Domain transfer, at that point namecheap shows an option to paste Auth Code,
Put that code into that field, and pay 10$amount to transfer and renewel - Done Thats it
your domain will be at namecheap in 3-5 working days
if you still need any assistance dear add me on skype