Is it appropriate for a single woman to be a mother?

...sperm donor, fostering, adoption etc.. (the question goes on to note).
(Take a deep breath, answer carefully...)  The first thing to say is that I know of single mothers who have done a great job, under the most challenging of conditions.  So this isn't a discussion about the capacity of a single woman to be a great mom.  The question is about 'appropriateness'.
Let's start with the idealised context for parenthood: two perfect people, a man and a woman, united in the covenant relationship of marriage.  There you go, it doesn't exist because nobody's perfect.  From that starting point, we are then talking about 'best-case scenarios' out of a whole pile of less than ideal situations.
I'm married, we have kids.  They are no doubt going to be afflicted with their parents' imperfections!  Yet, that's a better situation than if I were a single father, or if my wife were a single mother.  Two parents are often better than one simply because it takes a lot of hands to do nappies, washing, cleaning up, feeding and bathing.  Unless of course one parent is a complete layabout.
Now, if you're a single woman asking the question above, it might pay to think about why you're considering motherhood.  Is it about you and your needs/ wants/ desires?  Or is about serving others?  That's a quintessentially Christian question to ask.
That would be the difference between sperm donation or surrogate motherhood and adoption or fostering. The former smacks of being more about a self-centred desire to be a mother, the latter about serving children who need help.  'Service above self' is the Christian way to go.
I can think of situations where a single woman might serve by fostering or adopting kids, but, again, this is a best-case out of a pile of less-than-ideal situations.  In Australia, I suspect that it would be hard (probably impossible) for a single person to legally adopt or formally foster children.
Christian communities, families and friendships are so important in this area.  I know lots of single people who get so much from meaningful, lasting and 'parental'-type relationships with their friends' children.  (And it's great for the kids too.)  Hint: single people can make fantastic godparents.  Find ways of being included in single and family life.