Let's first establish that hygiene of this era has been misrepresented, from bodily cleanliness to specific aspects like dental hygiene. In many ways, the hygiene of the era was cleaner and more sanitary than our own modern ways. For instance, much of our dental issues now and need for dentists is caused by the consumption of sugar, something quite rare in the Georgian era and before.

While the toothbrush was not mass produced until 1780, there were ample methods for avoiding the toothpuller. The wealthier the individual, the higher the chances of avoiding the dentist (ie the local barber since there was not a need (until the introduction of sugar in the daily diet) to establish a dental professional), because their diet would be healthier, and they could afford such luxuries as tooth powder, toothbrush, and toothpick, all of which was custom made. Much like snuffboxes, cases for toothpicks, powder, and brushes were sought after and oft displayed.

The poor needed to devise their own methods, which didn't always work as well as they might hope (like substituting tooth powder with gun powder or soot). Homemade tooth powder and brushes were not difficult to craft if one didn't care to have a gold-handled brush with replaceable head (yes, really a thing). Who bothered to do so leaves much to be desired, I'm sure.

Diet is of the most important consideration for dental hygiene and good breath. While foul breath can come from poor teeth hygiene, it begins in the gut. An upset gut leads to foul breath. An upset gut is caused by a poor diet, especially one heavy in sugars and starchy carbs. It's really all related, as not only does the consumption of sugars and starchy carbs lead to upset gut, it also depletes the teeth of both enamel and nutrients, leading to plaque, decay, gum issues, etc., so a poor diet destroys gut, teeth, and breath all in the same fork-fill.

The wealthy, at least those not consuming a ton of sugar, would have had the best chance at good dental hygiene even without regular brushing since they had access to the most nutrient-rich foods. Nutrient-rich foods meant healthy gut, healthy bones, healthy gums.

The toothbrushes and tooth powder popular during the Georgian era are still popular today, although you'll not find them in the mass market shops. Both VanMan and Gaia Guy, for example, are companies that produce tooth powder and boar bristle brushes for those wishing to avoid synthetic and chemical-based materials. These modern products are, essentially, what our Georgian heroes and heroines would have used.

It's safe to say our heroes and heroines would have had strong teeth and healthy gums, would have brushed their teeth and had fresh breath, even if their teeth were crooked. We can't say the same for Mr. Collins, who might have taken to heart the suggestion that brushing should only happen every fortnight.

A great read on both dental hygiene and hygiene in general can be found here:

Golden Romance Research: Hygiene of the Georgian era