The following copies the first 1000 files found in the current directory to $destdir. Though the actual files depend on the output returned by find.
$ find . -maxdepth 1 -type f |head -1000|xargs cp -t "$destdir"
You'll need the GNU implementation of cp for -t, a GNU-compatible find for -maxdepth. Also note that it assumes that file paths don't contain blanks, newline, quotes or backslashes (or invalid characters or are longer than 255 bytes with some xargs implementations).
EDIT: To handle file names with spaces, newlines, quotes etc, you may want to use null-terminated lines:
find . -maxdepth 1 -type f -print0 | head -n 1000 | xargs -0 -r -- cp -t "$destdir" --