Well, by your own admission your dog was at large - the fact that it was the first time or an "accident" is irrelevant. I don't know what the fine or other penalty might be - you can call the number on the citation and ask what the likely outcome of a guilty plea would be or if you have other options. Once you have that information you can make a decision as to what to do.
If we do not have a signed fee agreement I am not your attorney and this is not legal advice.
I would need to know more facts about your case before I could answer your question. Whether or not to plea guilty is a serious decision that should be discussed with an attorney. In your situation, entering a plea of guilty and paying the fine could be harmless, but there could be unforseen circumstances in the future resulting from that plea.
Keep in mind, that entering a plea of guilty or going to trial are not your only options when charged with a crime/ordinance violation. Often times your lawyer can negotiate a plea with the prosecutor, or you can participate in a pre-trial diversion program so that the conviction stays off your record, which in your case could become important for possible homeowner insurance purposes or if your dog gets loose again in the future.
I would definitely speak with an attorney about your options. Local attorneys are always a great place to start with these type of citations, as they are familar with the prosecutors and law enforcement officers. Should you decide you may want to retain a lawyer, I also offer free consultations as well if you would like to discuss further.