Domain name delegation

[Frédéric Basse]

Hi,
I'm new on this newsgroup, I need an answer to a difficult question and
I hope you will be able to help me.
I run with some friends the website www.c.la which is a basic
redirection website.
Our bigger websites would like to keep the domain name but get rid of
the redirection which is bad for the SEO. Actually they would like to
use their subdomain (for instance website.c.la) with all the
functionnalities of a real domain (for instance website.com)
So I was thinking of delegating the zone files of bigwebsite.c.la to
the dns servers of a hoster.
This is common practise for instance when we buy a .com.
But I was told by an agency that it is not the same thing with c.la
because it is already a subdomain.
What is your opinion ?
I hope I'm clear, thanks a lot for your help.
Best regards,
Frédéric