A lot of the data processing is pushed to the database of the data source. Is that local to your machine, or is it on another server (such as a SQL Server running somewhere else)?
I typically run Tableau Desktop on a laptop and haven't noticed much in the way of performance issues. Most of my local data sources are small and not very complex (though some are). Many of the remote sources are relatively large and can be fairly complex. I do notice the fan running faster if I am telling Tableau to draw lots and lots of marks in view -- the graphics engine can definitely take some processing power.
Table calculations can also have an impact on performance and if you are using data extracts or local data sources any calculated fields could impact performance (except that row level calculations that are part of an optimized extract would have the results pre-calculated and stored as part of the data).
As with anything, more processing power, more memory, more storage, etc... can definitely make for a smoother experience -- but overall I haven't personally had any issues running Tableau on a laptop.
I do some pretty heavy stuff on a 3 year old Dell attached to mostly local files - it has been mostly fine
two short advices:
a. send tableau's logs to support team (firstname.lastname@example.org) to investigate crashes you reported here
b. upgrade to latest version 8.0.1
If your laptop runs with 6 or 8 Gbytes of RAM, then replacing it with a desktop could be a waste of time & cash as Joshua and Alex somehow underline already.