Any competent webmaster will be happy delaing with Anika`s suggestion, so I would go that route, register it yourself, so its yours
using 123-reg as an example they offer two options of linking your domain to a site,
the first one domain forwarding, (think telephone number forwarding) just hides your real domain name, eg you have me.alongdoma.moonfruit.com by using webforwarding, your customer can use your new domain name instead
the second is by pointing the domain name at the server your sites on, some diy site options offer that, the buzz word there is nameservers, some dont so you would have to use the first option, if you have a site built, your webmaster will tell you what nameserves to use, then you would just log into 123-reg, pop them in the two boxes, hit go and job done
of course there is always help here for both of the above if needed