I'm assuming the SB had you covered here since you didn't state his stack size. Your PF raise to $1.25 was fine for the average .10/.25 table, although it can vary depending on how tight the game is. Some .10/.25 games betting .50c will scare everyone out of the pot immediately no matter what, while others $1.25 will actually encourage more players to enter the pot hoping to hit big with any 2 cards. Remember that the PF raises really need to be adjusted according to the table playing style.
This leads me to the first problem I see with the hand. I don't see any type casting of the SB in this hand. Is this player loose-aggressive or solid-tight? What reads do you have on him if any? What hands have you seen him show after the river? What percentage of flops has he seen over the course playing? Does the SB over defend his blinds? etc.
These are just a few things that can help you with pre and post flop decisions against certain opponents. The answer to basically every NLHE question is "It Depends." In this case it really does depend on the playing style of your opponent.
The second thing is the Stack-to-Pot Ratio (SPR) and how it should have affected your PF action. The pot was about $4 PF and you had about $15 remaining. So your SPR is about 3.75. For an over-pair against a loose opponent who will commit all-in with a worse hand more often than not, a SPR of 3-4 is actually really good.
The problem with how you played the hand was the min-raise. You effectively committed half of your stack with your min-raise leaving yourself open to the hard decision of committing the other half after the SB went all-in.
In this situation against a very loose opponent I would have probably gone all-in unless I was fairly certain the SB had a set or KK, AA, both which seem unlikely. By doing this you put the draws to the hard decision of calling with only a draw and you maximize your profit against an under pair like AJ.
The third potential issue I see is your bankroll management. You said you reduced your online deposit to zero in a very short time. May I ask how much you deposited initially? To play the .10/.25 tables ($25 buying) you should technically have about a $500 bankroll to handle the swings, while a 600+ would be even better. The 5% rule is always a good starting point for new online players.
Finally, you're playing on Bodog. I used to play the .10/.25 and the .50/1 there and finally got fed up with all the ridiculous plays that the donkeys made in those limits at that site. I recently moved to PokerStars
and while the competition is definitely better my bad beats have significantly declined. Because honestly, going all-in for $16 in a .10/.25 game on a draw after calling a decent sized raise PF with 45s is fairly donkish. So I definitely have sympathy for you playing against the Bodog bunch.
In any case, definitely take a break if you lost your entire BR and perhaps try playing smaller tables to accommodate it in the future.