QChar contains an ushort as only member, so its size is sizeof(ushort).
In QString context it represents UTF-16 'characters' (code points).
So it's all about encoding here.
If you know your char const * is UTF-16 data in the same endianness / byte order as your system, simply copy it:
memcpy(q, c, 512);
If you want to initialize a QString with your const char * data, you could just interpret it as UTF-16 using QString::fromRawData():
QString strFromData = QString::fromRawData(reinterpret_cast<QChar*>(c), 256);
// where 256 is sizeof(c) * sizeof(char) / sizeof(QChar)
Then you don't even need the QChar q[256] array.
If you know your data is UTF-8, you should use QString::fromUtf8() and then simply access its inner memory with QString::constData().
Using QString with UTF-8 I don't know of any method to completely prevent heap allocations. But the mentioned way should only allocate twice: Once for the PIMPL of QString, once for the UTF-16 string data.
If your input data is encoded as UTF-8, the answer is No: You cannot convert it using Qt.
Proof: Looking at the source code of qtbase/src/corelib/codecs/qutfcodec.cpp we see that all functions for encoding / decoding create new QString / QByteArray instances. No function operates on two arrays as in your question.