Put some better debug stuff in the loop to see what is happening: $reader->read also reads closing tags.

use Data::Dump;
my $price;
while($reader->read) {
    next unless $reader->nodeType==XML_READER_TYPE_ELEMENT;
    dd $reader->localName, $reader->readInnerXml;
    $price = $reader->readInnerXml if $reader->localName eq 'price';
}
dd "price", $price;
[download]

Output:

(
  "product",
  "\n<name>5 Spoke Wheel</name>\n<description>Reconditioned OEM</descr
+iption>\n<price>123.45</price>\n<url>http://www.foo.com</url>\n<image
+url>http://www.foo.com/foo.jpg</imageurl>]\n",
)
("name", "5 Spoke Wheel")
("description", "Reconditioned OEM")
("price", 123.45)
("url", "http://www.foo.com")
("imageurl", "http://www.foo.com/foo.jpg")
("price", 123.45)
[download]

BTW your XML is broken. </buyurl> should be </url>.