Nothing stops you from practicing as an agent. The law degree is mostly useful if you want to make partner at a firm or expand into other areas such as trademarks or litigation. Salaries are higher for patent lawyers than patent agents. Some firms will refuse to hire agents either because they believe that engineers can't write or can't be efficient. You also get more respect as an attorney than as an agent, particularly in a law firm. If you are not 100 percent focused on patent prosecution, it might not be worth the time investment in law school, particularly if you already have work. Maybe not yet anyway. If you decided you want a full time career in patent law, law school would make sense. The big money is in partnership at a law firm and you can't make partner as an agent. And you would be unlikely to make partner working part time. There are firms in Canada that are all agents but that is another story.
I would say you would want to practice at least two years with someone experienced and write 100 applications or so before considering going on your own. Some would say it takes six years of full time practice to become really good. To get a good head start, take as many Kayton courses as you can after the patent bar. Patent law is highly complex as the Federal Circuit seems to keep coming up with new ways to limit the scope of patents. You have to keep adjusting the way you draft applications in view of the evolving law, and have to keep up with the law. When I first starting practicing, there were some attorneys who thought "means for" claims were the greatest thing since slided bread. Then came the Valmont case and others that drastically limited the value of means for claims and many attorneys did not use means for language at all. Then, more recently, came Festo and cases drastically limiting the doctrine of equivalents so that now people are thinking maybe there is some value to the structural equivalents you get with "means for" claims as these might provide literal infringement.
To write cases for others, you'll have a lot of startup expenses such as a good docket system (preferably dual docket systems), a time and billing system, trust account software, accounts payable software (if you want) and malpractice insurance. Expect to pay $3500-10,000 per year for malpractice insurance, and read the exclusions. There have been some high patent malpractice judgments, making it harder to get malpractice insurance. There was a 30 million dollar award against Fish & Richardson; and Foley and Lardner was sued for even more. AND THESE ARE GOOD FIRMS. If it could happen to them, it could happen to anybody. You'll probably want to hire a paralegal so that you have two people watching the dates--it is easy to get distracted by the day to day work and pressing deadlines, and it makes sense to push the lower skill work such as document assembly and filing to a lower paid person. Part time may turn into full time when office actions start coming years down the road. With this overhead, you'll need a certain volume of work to make it worthwhile. Or you could see if a firm with a good docketing system would do the docketing and receive the mail for you for a fee. There is also at least one docket company that will receive the mail for you and scan it in, but that service does not come cheap.
These are just some thoughts. The short answer to your question is that you do not need a law degree unless you want to be in a law firm. You should seek a lot of training, though.