The events of TPM describe the first appearance of a trained Sith warrior (Darth Maul) in quite a long time. All the members of the Jedi order seem to be concerned about resolving the "Sith mystery" that stands behind this. So, the question is, why send Qui-Gon and Obi-Wan who are clearly not as powerful compared to other Jedi (Obi-Wan is still a padawan to this moment) on a mission to protect Queen Amidala? Nothing really important was happening at that point in time - Yoda and others just seem to be idling. Why take this risk? Why not choose a more capable Jedi to handle this if they didn't really know how powerful Darth Maul could be?
There are multiple answers to your question:
First, Qui-Gon is quite "powerful" at the time of The Phantom Menace. It is said in the film that, had he followed the code of the Jedi perfectly he would have been on the High council. So clearly he's not your average Jedi. As for Obi-Wan even if he was a padawan at the time, his training was soon to be complete. Indeed at the end of The Phantom Menace Obi-Wan is made a Jedi knight. So we have one confirmed Jedi who has the power to be on the high council and his "soon to be knight" padawan. It is a quite powerful team to investigate on...
Second, a "mystery". The Jedi order does not have proof of anything at the start of the events. They just feel that something is wrong. In this kind of case it make sense to not send the best Jedi on the case. But they still take seriously enough to send one of the best Jedi outside the high council.
Third, discretion. Protecting Padme Amidala was not the principal mission. At first it was to find a diplomatic solution to the blockade on Naboo. The investigation of the "Sith mystery" was supposed to be done discreetly. Sending a member of the high council is quite the opposite of discretion and could spook off the Sith before they can do anything.
Fourth, you don't know what the high council is doing. The blockade is a major political issue. It would make sense that the council is mostly focused on resolving this issue
To add a few points to the above answers:
The primary reason the Jedi were sent was to peacefully/diplomatically deal with the blockade, and later as protection/defenders for Amidala. Both Jedi are actually more than adequate at dealing with the blockade, even when diplomatic measures failed. (as I'm sure the council at least suspected they might, otherwise, why send Jedi in the first place?)
The blockade, the war, the Trade Federation robots, didn't stand a chance against the Jedi, in fact, had Darth Maul not been there, everything would have gone very well and a happy ending for everyone, including Qui-gon.
Qui-gon was actually one of the best lightsaber duelists of the order, and obi-wan goes on to be one of the best swordsman in the order ever. Obi-wan successfully defeats Maul, then goes on to match Dooku head-to-head and hold him off until Yoda gets there, then again handles a battle with Dooku, this time defeating him with Anakin, and then later defeats General Grievous, and later again defeats Anakin. There's no indications that either of these characters are poor swordsman/duelers, they were both top of their game, so there's no reason to suspect the Council made a poor choice.
Qui-gon and Kenobi were far more tired than Darth Maul; they've been fighting all day long, leading rescue efforts, they're physically and mentally tired. Darth Maul was silently waiting, planning a trap for them. There's a big difference in energy levels.
Qui-gon's fighting style was Ataru, which is acrobatic, energetic fighting, relying on high physical energy levels, which he didn't have as mentioned above, open spaces, which they didn't have in this particular fight, and acrobatics, something Darth Maul was equally as good at, if not better than Qui-gon. This means one of Qui-gons primary advantages over other foes was negated here.
Also, Qui-gon's fighting style was Form IV/Ataru as mentioned above, a defensive, open-area, evasive, fighting style. Extremely good at maneuvering and blocking ranged attacks; not as good at close-combat fighting. Obi-wan's fighting style was Form III, very good at close-combat fighting, when paired together, that makes a really deadly combination; one Maul probably couldn't have lived through, and would have left both Jedi alive. Maul intentionally tried to restrict them by pulling them into a situation that would limit Qui-gon's fighting style, and split the two Jedi, allowing him to deal with them one at a time. Neither Qui-gon Jinn, or Kenobi could have possibly foreseen this, and the Council, even if it suspected they might have to deal with an unknown Sith, also probably didn't expect two of its best fighters, to be ambushed while physically and mentally exhausted, split up from each other, and forced to fight in a restrictive environment.
To add to this, everyone was "shocked" at Qui-gon's death. This means despite them being aware of a mystery Sith, no one expected that mystery Sith to best Qui-gon/Kenobi together.
I don't think that the Jedi Council felt how dangerous the mission, nor how powerful Darth Maul would be. Qui-Gon Jinn was already the Jedi that had been on the mission to Naboo and had already developed a working relationship with Queen Amidala so it was logical that he continue the mission (and Obi-Wan as an apprentice goes where Qui-Gon goes).
Also, the Jedi Council didn't foresee the dangers, as Jedi Master Ki-Adi-Mundi recorded in 32 B.B.Y. (as it appeared in the book "Jedi Vs. Sith: The Essential Guide to the Force, page 209):
It is little consolation that every member of the Jedi Council was surprised by recent events: the discovery of Skywalker, the death of Qui-Gon Jinn, and the return of the Sith."
Reasons are mostly artificial, i.e. out of universe
Story revolves around Anakin, and Obi-Wan has to become his master. But, Obi-Wan is still young, so he has master of his own. Therefore, he must lose his teacher (Qui-Gon Jinn) and Anakin has to have bond with him, so Jedi Council would have a reason to select Obi-Wan as a master of Chosen One . This of course sets further narrative: Obi-Wan lacks experience so he fails to train Anakin properly etc...
In-universe, case for giving Chosen One to 25 year old newly minted Jedi Knight is already slim, so they had to cut some corners. If they sent full Jedi strike team (which would be logical, even for not-so-smart Jedi Council), Obi-Wan would either remain padawan for some time, or Qui-Gon Jinn would become Anakin's master. It is worth to mention that Qui-Gon Jinn already fled once from Darth Maul on Tatooine, so Jedi did know he was weaker then Sith. But, as I said, corners had to be cut, and Episode 1 is not among best stories in SW universe.