Notes of the red protector issue are so rare that they are collected only by type, not by date. (That is the case for any manuscript dated rare note; date collecting is popular for notes where the surviving population is sufficient to support it, such as the first issue Westmorlands)
There are more of the $4 denomination known than all the other denominations combined, ie. 1x1846, 2x1851, 2x1852, 3x1856.
It is known from documentary evidence that the first printing orders for this series began in 1843, but the first $4 sheets were not ordered until April 1844.
Surmising the condition of the note from the image of the face in this thread, I would suggest a fair and realistic market value would be something of the order of $4,500, perhaps a little more. This is well in advance of the present catalogue value, and is based on recent sales of Bank of UC notes in general. The 1846 date is not a factor; type and condition will determine the price.
Incidentally, what is the evidence that numbering started at 10000 for this issue? Numbering was sequential from beginning to end of the issue, and since it is pretty clear that $4 notes were issued earlier than 1846, are we to believe that fewer than 20 notes were issued before Dec. 1846?