Why don't I just do the work myself and save money?
Do It Yourself Transfer of Old to New Domain
The experience of transferring from old to new domain if done properly will make you appreciate how search engines work on indexing your site, ranking, and linking.  The word there is “if done properly.” Unless you have sound technical knowledge, it is not advisable to work on it alone.  It is much more complicated than it seems. Technical problems are sure to crop up and if not handled properly could lead to other problems and make matters worse.  There are some who made workarounds by keeping the old one operating parallel to the new domain.  Search engines might see content as duplications and penalized both sites for it.