AAA credit rating really doesn't mean all that much, but if you put stock in it, Fitch upgraded Australia to AAA in 2011 - substantially after Howard left. Here's another relevant link: http://www.smh.com.au/federal-politics/political-news/hey-big-spender-howard-the-king-of-the-loose-purse-strings-20130110-2cj32.html
By the IMF's judgement, Howard was the most profligate spender in recent history, which is shown pretty clearly in this graph: http://www.treasury.gov.au/~/media/Treasury/Policy%20Topics/Taxation/Pocket%20Guide%20to%20the%20Australian%20Tax%20System/Downloads/Pocket_tax_guide.ashx (Chart 2). Tax receipts and government spending both went down significantly in 2007 after Rudd took over - even taking into account accumulated (necessary) infrastructure maintenance expenditure that was generally left to the side during the Howard era, and even though this period encompassed the GFC.
"Got us out of debt" is a pretty shallow glance at the situation. How did Howard manage to do this, while being both higher taxing and higher spending than the 07-13 government? Well, this is how: http://www.finance.gov.au/property/asset-sales/past-sales.html (Howard was in 96-07, so anything between those dates was generally driven by him and Costello).
Some key ones: Phase 1 Airports Melbourne Airport Brisbane Airport Perth Airport $3.337b
April 1998 Phase 2 Airports (Adelaide; Alice Springs; Canberra; Coolangatta; Darwin; Hobart; Launceston; Mt Isa; Parafield; Tennant Creek; and Townsville; Archerfield; Jandakot and Moorabbin) $730.8m
June 2002 Sale of Sydney (Kingsford Smith) Airport ($1355m of SACL debt repaid in addition) $4.233b
July 1996 Commonwealth Bank Secondary Public Share Offer (3) and share buy back $5.1b
And the big three:
November 1997 Telstra 1 $14.2b (plus $3 billion payment to the Commonwealth from retained earnings) October 1999 Telstra 2 $16.0b November 2006 Telstra 3 $15.4b
For a grand total of approximately $62b. Turns out it's pretty easy to "get out of debt" when you sell $62b worth of stuff. Now, some of that were generally loss-makers and only turned a profit after being privatised. Some of them were profit-makers (CBA, Telstra) and were a massive long-term loss to the nation (both its tax coffers, and general services). Turns out selling your entire communications network for a pretty low price is a bad idea. And then there's this, too: http://www.theaustralian.com.au/news/nation/reserve-banks-gold-sale-cost-us-5bn/story-e6frg6nf-1225985231872
Howard and Costello picked up this image of being magical economic managers, and I'm not entirely sure where. At best, they were merely competent - but you could pretty easily make a case that they did substantial long-term damage to the Australian economy in the time they were in. Between the sale of long-term profit-makers for short-term gain, and the 50% capital gains tax discount (which did horrendous things to our property market), blugh.