"If they had the same size network, it would take 60 confirmations on DOGE to match 6 confirmations on BTC. If you are OK with 30 confirmations on DOGE, you would be OK with 3 confirmations on BTC."
That's not actually true. Satoshi actually provided code in his original paper to calculate this which I've just run, and it turns out that if, say, an attacker controlled 30% of the total mining power of each network during their attack they'd have a 33% chance of successfully double-spending against BTC with its 3 confirmation requirement and a 0.015% chance of successfully double-spending against DOGE with its 30 confirmation requirement. That's a big difference.
Let's suppose we decided to take advantage of this to require less confirmations on DOGE, say 10. Then the chance of a successful double-spend goes up to 4%, still lower than Bitcoin. Of course, let's be generous and assume our attacker now has three times the opportunities to double-spend, upping that to a 12% chance of success. It'd still be safer to accept transactions with 10 confirmations taking 10 minutes on same-size-DOGE than ones with 3 confirmations taking 30 minutes on BTC.
Actually, it looks like if we give our attacker those extra attempts provided by a faster attack for free, 8 one-minute confirmations are at least as secure as 3 ten-minute ones for any size of attacker that BTC can realistically defend against at all. (And remember, we're already talking about attackers powerful enough that 3 confirmations in BTC isn't safe. If we assume a hacker with 10% of the total mining power, which is arguably all that 3 confirmations can realistically protect against, 5 DOGE confirmations are enough and take half the amount of time as a single BTC confirmation)