Such words are obviously new and therefore subject to fairly rapid evolution, but in this case "webdesigner" has long been written as two words and would seem odd as one.
From the Oxford English Dictionary, Draft Partial Entry 2001
Originally written with a capital initial, web compounds are now
increasingly written with a lower-case w. Since it is difficult to
make an objective judgement about the dominant capitalization in
particular cases and the evidence is changing too rapidly for such a
judgement to be of any lasting value to the reader, the compounds
below have been routinely presented with a lower case w irrespective
of the quotation evidence.The patterns of attachment are less
inscrutable. The relative dominance of one-word, hyphenated, and
two-word forms is in general governed by the status of the second
element. Those compounds in which web is combined with a word
occurring independently as a common noun are most frequently written
as two words (web page, web site). Blends with parts of other words
are typically rendered as one word (webliography, webzine).
Hyphenation occurs most consistently where the second element is an
adjective or is frequently found in compound formations (web-aware,
web-based, web-enabled). a.a General attrib., as web access, web
address, web design, web designer, web developer, web publisher, web
publishing, web surfer, web surfing, etc.