Pretty good article here from a banking trade rag:
http://www.americanbanker.com/magazine/124_02/why-bitcoin-matters-for-bankers-1065590-1.html
I have to say, this is probably the first somewhat "mainstream" (i.e., not tech-oriented) publication that I have seen which actually understands how Bitcoin works on several levels, and has a full and nuanced and forward-looking view of Bitcoin. Not just the coins, but the technology as a whole. The author sees the blockchain idea being used in "real" banking someday. Hell, just this image is probably the best "in a nutshell" Bitcoin explanation I've ever seen.
Confirmation depends on that transaction being used in a Block. Until it shows up in a Block, it might have propagated throughout the network (so both the sender and recipient can see it), but it will still be "Unconfirmed".
Some people/clients/whatever will not count it as "confirmed" until it has been included in a block, and that block has been confirmed in the blockchain several times over. (Commonly 1 extra block, 4 extra blocks, 10 extra blocks... depending on trust between sender and recipient, and value of the amount sent.) This is due to the possibility of orphaned blocks and the short-term forks that can happen due to them. (2 miners find a block at the same time; one of the blocks is reported to part of the network, the other block is reported to another part of the network... then the network figures out that it's got 2 different blocks floating around, and the majority rules as to which block was the real one, and which direction the fork should take.) When an orphaned block occurs, theoretically your transaction should be included in both the orphan block and the true block; but sometimes it might only be included in one or the other. (Or neither; but in any case, it should show up in a block soon.) (Miners can pick and choose which transactions to include in a block; paying a transaction fee bribes the miners to include it as early as possible, if it is not a high priority transaction. (High priority transaction usually meaning old bitcoins that haven't been moved around recently. This is to prevent blockchain spam, where 1 person could just send back and forth tiny amounts of BTC over and over again to millions of addresses.))
In any case, the block time of the network will determine how long it takes to confirm (whatever definition of confirm you choose). BTC is designed to have block times of 10 minutes on average, but it can go as low as a few seconds (somebody gets very lucky) or as long as 40+ minutes (the whole network has bad luck). I know I've seen BTC blocks in the 10-second range, and as I write this, miners have been working on the current block for over 30 minutes.
So DOGE transactions will be confirmed more quickly than BTC or LTC. It doesn't directly have anything to do with the network hashpower. It has to do with the block rate, which is programmed into the code by the designer of the coin, and which affects the difficulty scaling to match the hashing power of the network.
So, I suppose if a coin had a long difficulty reset period (like BTC = 14 days) and it were on a low difficulty but had a lot of hashpower come in, the blocks would come in quicker on average, which would speed up confirmation time. But as soon as the difficulty resets, it should go back to 10 minutes. (In the case of Bitcoin.)
That being said, it would be smart to require more blocks for confirmation for DOGE than for BTC or LTC. Since the blocks come so fast one after the other, there is a greater chance for an orphan or a short fork with DOGE.