You can do it all in one shot on the commandline. I've used this method to copy an entire database from one server to another.
First, create an empty database on your target server. Then, pipe the dump output of your source database into the target host's database like so:
mysqldump -h<src_host> -u<src_user> -p<src_pass> -q <database> | mysql -h<targ_host> -u<targ_user> -p<targ_pass> <targ_database>
The -q options is the "quick" option, which means output is dumped immediately to stdout without being buffered in memory first. Generally speaking, you'll always want to use the -q option when dumping large amounts of data.
Take care,
Nik
http://www.bigaction.org/