Taking a search through Ubuntu's APT system, to see whether any IDN related tools are available...

$ apt-cache search punycode

libidn11 - GNU Libidn library, implementation of IETF IDN specifications
libidn11-dev - Development files for GNU Libidn, an IDN library
idn - Command line and Emacs interface to GNU Libidn
libidn11-java - Java port of the GNU Libidn library, an IDN implementation
libidna-punycode-perl - encodes Unicode string in Punycode

There's the idn package!  Which allows encoding of IDNs in punycode in the command line...

Doing an install...

$ sudo apt-get install idn -y

And trying it out!

$ idn правительство.рф

libidn 1.15
Copyright 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009 Simon Josefsson.
GNU Libidn comes with NO WARRANTY, to the extent permitted by law.
You may redistribute copies of GNU Libidn under the terms of
the GNU Lesser General Public License.  For more information
about these matters, see the file named COPYING.LIB.
xn--80aealotwbjpid2k.xn--p1ai

And resolving the domain...

$ nslookup xn--80aealotwbjpid2k.xn--p1ai

Non-authoritative answer:
Name:	xn--80aealotwbjpid2k.xn--p1ai
Address: 95.173.135.62

Note that resolving the domain directly results in rubbish!

$ nslookup правительство.рф

Non-authoritative answer:
Name:	\208\191\209\128\208\176\208\178\208\184\209\130\208\181\208\187\209\140\209\129\209\130\208\178\208\190.\209\128\209\132
Address: 67.215.65.132

So, basically from this we understand that applications will need to use the punycode encoded version of the IDN, NOT the original IDN, when resolving.  And there're tools out there already can do that for us.

Since Ubuntu has these packages, Debian would also have the corresponding packages available too.