Of course you can use your account on 2 computers, lots of people use Fiverr at home on their desktop and from a laptop or tablet or phone while they travel or hang out in a coffeshop or whatever. Fiverr doesn´t care about how many devices you use, only that you don´t have more than 1 account.
And this doesn´t have anything to do with the level you hold.
The only possible problem that could arise is if you use a shared internet connection on your laptop while you´re away and if other people use the same connection for logging into their Fiverr accounts, because that might trigger some alarm for potential multiple accounts. I´ve logged into my Fiverr account away from home and through various WiFis and never had a problem yet, which doesn´t mean that there never will be a problem, though.
If it makes you feel safer, you could write to Customer Support and tell them that you intend to log into Fiverr from your laptop too and away from home, they´ll surely tell you it´s no problem.