Sand - 3:08 pm on Jan 22, 2013 (gmt 0)
Yes, the bad links will follow you if you simply redirect the entire site. Don't do it, unless you want the new domain to have a similar fate. You have a few options.
1. Did you have any interior pages that earned quality natural links but don't have a lot of spam links pointing at them? If so, 301 those pages to the equivalent on the new site.
2. Don't redirect the homepage (assuming it was the target of your bad links), but put a link on there to your new domain, notifying your visitors that you've moved. This *might* satisfy the branding concerns, and will at least send you some referral traffic.
Basically, you want to preserve any natural value being passed to interior pages, without passing on the negative things that have been done to other pages. So a wide sweeping 301 redirect will likely hurt you. You have to be a surgeon on this one.