1. There is a feature in the Authorize.net virtual terminal that will allow you to export the transactions to IIF files that you can then import to QB. Here is a link that discusses it http://support.quickbooks.intuit.com/support/Pages/KnowledgeBaseArticle/bde7b06f
2. QB Webconnector API – never used this option but I heard others have used it successfully to move transactions from their cart to QB
3. QB API – We developed a C# program that exported customer and orders info from our shopping cart and imported it to QB using their API.