Question: "I know virtually nothing about rugs and was wondering if someone can help me find out what type of pattern/design this is?"
Answer: Some very good answers on the forum which we completely agree with the comments. "Lotto Uskak" design was mentioned as well as another regarding floorcovering being a fabric as opposed to a carpet.
While some rug designs and styles are very distinguished and clearly indigenous to particular regions, overall, evolution of rug designs has naturally been very eclectic. Motifs and patterns migrating from one region to another, borrowed from one and inevitably brought to another. With this, the search can become very diffilult to isolate what terms may be useful.
Antique Ushak designs is a very good suggestion and absolutely a good contender as being similar in motif. The other point made was the rug may not be a rug at all, but more likely a fabric, which would explain the absence of a border and repeating pattern. This is probably true in the photograph above: Likely a printed floorcovering or broadloom carpet of sorts.
Printed floorcoverings are not as common as they once were in the late 18th and early 19th centuries, especially in the New England area of the US. Canvas 'carpet' was significantly less costly for higher traffic areas than woven fabric as painted designs and motifs lost to fading or use could be revitalized with much less expense than actual woven material.
The repeating motif of the carpet above, as well as the lack of a border may also serve as an indication of broadloom carpet as previously mentioned. This too was available many, many years ago. Examples may be seen in historic landmarks such as the Lincoln Bedroom, where long strips of carpeting would be sewn together to the size to the area.
The best search will probably be using keywords relevant to the motif as opposed to searching any specific type of rug. Looking at the pattern, the repeat is diamond-shaped in equal incriments at fairly similar scale. In rugs, this would sometimes be referred to as a "lattice" or "panel" motif (to a certain extent). Perhaps "lattic rug" "lattice carpet" would be good starting points, as would "panel rug" or "panel carpet" and perhaps "ingrain rug" "ingrain carpet". Very old examples from the Safavid period sometimes inspire newer, modern renditions, so other choices could be "vase carpet/rug," Although many may be more geometric than the scalloped edges of this motif above, hopefully it is a good start. Another great possibility would be to search local wall-to-wall or broadloom locations near you. This may be a great option as they typically come without borders, and may be made in to custom area rug sizes. Often, there is a minimum size order, although would be great if you have other areas of your home to decorate with similar style. If you want to go a more authentic route, there are many retail design studios of Tibetan rugs and Indian carpets who have the ability to make custom hand knotted rugs. The final result could be virtually identical to the carpet above, made to your exacting specifications.
Great looking carpet, we wish you the best of luck!