She had a slight bleed and a brownish discharge, then it turned out that she was pregnant. Should she make up missed prayers?

The fuqaha’ differed as to whether a pregnant woman can
menstruate or not. There are two opinions, the soundest of which is that
she can menstruate, although this is rare among women. This is the view of
the Maalikis and Shaafa‘is, and of Ahmad according to one report; it was
also regarded as more correct by a number of scholars. But the scholars
stipulated that in order for the blood that comes from a pregnant woman to
be regarded as menstruation (hayd) it should be like menstrual blood and
come at the time of menses. Please see the answer to question no.
23400. 

Based on that, it seems that what happened in your case was
not hayd (menses). 

With regard to making up the prayers, you do not have to make
them up, because you only refrained from praying because you thought that it
was a period (menses). 

Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him)
said: This also includes the woman who experiences istihaadah (non-menstrual
bleeding) if it continued for a while and she did not pray because she
thought that prayer was not required of her [at that time]. There are two
opinions as to whether she has to make it up, one of which is that she does
not have to do so — as was narrated from Maalik and others — because when
a women suffering from istihaadah said to the Prophet (blessings and peace
of Allah be upon him), “I have been bleeding heavily for some time and it
prevents me from praying and fasting” he instructed her as to what was
required of her in the future, and he did not instruct her to make up past
prayers.

End quote from Majmoo‘ al-Fataawa, 21/101. 

And Allah knows best.