Am I able to download my shipment data?

You can!  Shipment data is able to be downloaded as a CSV file in a couple different locations.

Shipments page: To download your data from the shipments page, click on "Export" in the upper left (shown below).

This will trigger the download.  From there, you can open your CSV in Excel, Google Sheets, or whatever medium you typically manage your spreadsheets in.  Note - Since this is a CSV file, it will not necessarily be formatted and will require you to manipulate it to your desired view. 

One benefit from downloading this file from the shipments page is that it enables you to filter the data you want to download beforehand (see below).

The downloaded CSV will only include data respective to the filters you've selected. Note - The column orders in the CSV file may not stay in the same order as the filters appear in the Shipments page.

Another advantage of downloading the file from the Shipments page is that it will automatically respect any customer visibility restrictions/filters.  Reps assigned to particular customers or teams will only be able to view the data of those to which they've been assigned.  

Settings > Data: A CSV of shipment data can also be downloaded by going to your Settings, then clicking on "Data".  Note - This is only available to account owners, and will be a download of all shipment data (in other words, not filtered).